A doubly-fed generator fault diagnosis method based on multi-source data and transfer learning

By using multi-source data and transfer learning, a fault diagnosis model for doubly fed wind turbines was established, which solved the problems of insufficient model generalization ability and insufficient data, and achieved rapid and accurate fault diagnosis and self-correction capabilities, adapting to various fault types.

CN115392115BActive Publication Date: 2026-05-19NORTHWEST ENGINEERING CORPORATION LIMITED
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
NORTHWEST ENGINEERING CORPORATION LIMITED
Filing Date
2022-08-05
Publication Date
2026-05-19

AI Technical Summary

Technical Problem

Existing fault diagnosis technologies for doubly fed wind turbines suffer from problems such as insufficient model generalization ability, lack of data, insufficient model training data, and low diagnostic efficiency due to small and variable data volume.

Method used

By employing multi-source data and transfer learning methods, a sample relationship network and a prior knowledge network are established through multi-source data collection and preprocessing. Feature combination and multi-classification model construction are then carried out. Combined with community detection and hierarchical clustering, a motor fault transfer diagnosis model is formed.

Benefits of technology

It enables rapid and accurate fault diagnosis under different operating conditions, reduces hardware investment, improves diagnostic efficiency and reliability, has self-correction capabilities, and adapts to various fault types.

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Abstract

The application relates to a doubly-fed generator fault diagnosis method based on multi-source data and transfer learning, S1, multi-source data collection and preprocessing, operation data of different data sources are collected, and the operation data of each data source is preprocessed; S2, prior rule knowledge acquisition, a prior knowledge base is formed; S3, multi-source data and rule transfer learning, basic data sets of fan fault detection are obtained; S4, feature group model division, feature grouping is realized; S5, multi-classification model building, after training, multi-classification results of faults can be obtained, a motor fault transfer diagnosis model is formed, and data in a use process is input into the motor fault transfer diagnosis model to diagnose and predict faults. The application is convenient for predictive maintenance of a system, experience of different sites and different projects can be referred to, and hardware investment is maximally reduced. A multi-model multi-working-condition mode is adopted, a sample library and a prior knowledge base are formed, and a foundation is laid for operation of a later related system.
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Description

Technical Field

[0001] This invention belongs to the field of wind power generation, specifically relating to a fault diagnosis method for doubly-fed generators based on multi-source data and transfer learning. Background Technology

[0002] Currently, there is a wealth of research on fault diagnosis technology based on doubly-fed induction generators (DFIGs). This has significantly reduced the time and cost of fault detection and maintenance. However, current research still has several limitations, such as: 1. Most studies only focus on diagnosing one or similar types of faults, resulting in weak model generalization ability. Research on multi-classification problems involving multiple faults is relatively scarce. 2. Data required for model training is lacking, operational data collection is difficult, and fault conditions are even rarer. Most model training work only focuses on limited operational data or simulation data, lacking the integration of various data and rules. 3. Most models fail to address issues such as limited data volume and data decay and variation during operation. Summary of the Invention

[0003] This invention discloses a fault diagnosis method for doubly-fed generators based on multi-source data and transfer learning, which can cope with multiple operating conditions, has self-learning capabilities, and can build, train, and self-optimize fault diagnosis models by drawing on various rule knowledge.

[0004] A fault diagnosis method for a doubly-fed generator using multi-source data and transfer learning includes the following steps:

[0005] S1. Multi-source data collection and preprocessing: Collect operational data from different data sources and preprocess the operational data from each data source.

[0006] S2. Prior rule knowledge acquisition: Using the associated features collected from actual samples as keywords, literature is collected and mined to form a literature set. Based on the literature set, relationships are extracted through natural language processing and entity recognition methods, and a prior knowledge base is formed with keywords as the core.

[0007] S3, multi-source data and rule transfer learning, for each sample dataset, builds a model based on within-group data, using features as nodes and relationships between samples as edges, forming a network of relationships between features, i.e., a sample relationship network.

[0008] Based on a prior knowledge base and a corresponding sample relationship network, a prior knowledge network is constructed, i.e., a specific network is created.

[0009] Based on sample relationship networks and prior knowledge bases, different complex networks are built using different data sources, forming several sub-networks with features as nodes and relationships as edges.

[0010] For the several sub-network sets formed, a similar network fusion method is used to fuse the networks, resulting in a complex network containing different network features and fault relationships at different levels, which serves as the basic dataset for wind turbine fault detection.

[0011] S4. Feature group model partitioning: Community detection is performed on the fused model. Hierarchical clustering, elbow statistics, or silhouette coefficient method are used to optimize the number of cluster centers to obtain the final number of cluster centers. Based on this clustering result, the grouping relationship of features is determined, thereby realizing the grouping of features.

[0012] S5. Multi-classification model construction: Based on the above feature grouping results, a two-level mapping model is set up. In each community, a preliminary mapping model is established. Each community combination forms a combined feature value. Using such combined feature values ​​as input, a higher-level mapping model is further built. After training, multi-classification results of faults can be obtained, forming a motor fault migration diagnosis model. The data in the process is input into the motor fault migration diagnosis model to diagnose and predict faults.

[0013] In the multi-source data collection and preprocessing, data cleaning is performed on each subset of data, i.e., the data within a single data source, to remove features that cover less than 70% of the sample size. Samples with less than 70% coverage of features are removed. Coverage detection is not performed between different data sources, and subsystems in overly sparse subsets are eliminated.

[0014] In S2, after collecting and mining the literature, a comprehensive evaluation index is constructed based on the journal in which the literature is published, the number of citations, and the author's institution. Based on this, the literature is sorted, and the literature with the lowest ranking is removed to form a literature collection.

[0015] Following S3, data supplementation is performed. For the same dataset, statistical analysis of data volume, positive and negative examples, and features is conducted, along with balance detection. For datasets with significantly fewer data points and fault types with poor balance, data supplementation is performed based on the simulation model. During the data supplementation process, the data is gradually increased by 10%, 20%, 30%, up to 100%, and statistical analysis is performed. At the same time, the significance of features and the correlation between features are monitored. When the deviation exceeds 5%, the supplementation of simulation data is stopped.

[0016] Following S5, system verification is performed. Based on the motor fault migration diagnosis model in S5, motor faults are diagnosed. A simulation incremental model is built using actual data based on the steps in S5 to diagnose motor faults. When the difference between the motor fault migration diagnosis model and the simulation incremental model is greater than 5%, the actual data is added to the basic dataset to update the basic dataset, and the new basic dataset is used to update the motor fault migration diagnosis model.

[0017] The preprocessing in S1 includes normalization of the data within the dataset and outlier removal.

[0018] In S3, the sample relationship network is represented as G. similarity = (V, E), where node V corresponds to the data at each time point, and edge E corresponds to the similarity weight between samples. Sample similarity is represented by an n×n similarity matrix W, where W(i,j) represents the similarity between samples. The prior knowledge network is G. prior = (V,E′), where edge E′ corresponds to the similarity weight between samples. The sample similarity is represented by an n×n similarity matrix W″, W″(i,j)=(1-α)·W(i,j)+α·W′(i,j), where α is the weighting coefficient, and W′(i,j) is obtained by multiplying the first weight matrix formed by the frequency of rule occurrence in the prior knowledge base in S2 and the second weight matrix formed by the rule weights in the expert weight base.

[0019] The beneficial effects of this invention are as follows:

[0020] 1. Cost savings: It facilitates predictive maintenance of the system and allows for the application of experience from different sites and projects, minimizing hardware investment.

[0021] 2. Efficiency Improvement: This method enables online operation, reduces troubleshooting time, quickly identifies the source of the fault, and restores production as soon as possible.

[0022] 3. High reliability: It features historical data backtesting, incremental data correction, and simulation model identification. It has a stronger self-correction capability than conventional systems.

[0023] 4. Based on the relatively short time series of current operating data and the difficulty in collecting fault condition data, this paper improves the difficulty of integrating operating data from multiple sources.

[0024] 5. It provides processes and methods for the comprehensive utilization of rules and data from different sources.

[0025] 6. A multi-model, multi-condition approach was adopted, and a sample library and prior knowledge base were formed, laying the foundation for the operation of related systems in the later stages. Attached Figure Description

[0026] Figure 1 A schematic diagram of the fault diagnosis method for doubly-fed generators based on multi-source data and transfer learning;

[0027] Figure 2 A schematic diagram illustrating the construction of a multi-classification model;

[0028] Figure 3 This is a schematic diagram of the system verification process;

[0029] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Detailed Implementation

[0030]

Example 1

[0031] like Figure 1 As shown, a fault diagnosis method for a doubly-fed generator based on multi-source data and transfer learning includes the following steps:

[0032] S1. Multi-source data collection and preprocessing: Collect operational data from different data sources and preprocess the operational data from each data source.

[0033] The preprocessing in S1 includes normalization of the data within the dataset and outlier removal.

[0034] In the multi-source data collection and preprocessing, data cleaning is performed on each subset of data, i.e., the data within a single data source, to remove features that cover less than 70% of the sample size. Samples with less than 70% coverage of features are removed. Coverage detection is not performed between different data sources, and subsystems in overly sparse subsets are eliminated.

[0035] First, data from different data sources, i.e., data from different factory sites, are collected. Data from each factory site is considered a data source. Data from each data source is normalized and outliers are removed within the dataset.

[0036] Next, each subset of data, i.e. the data within a single data source, is cleaned to remove features that cover less than 70% of the sample size and samples that cover less than 70% of the sample size.

[0037] No coverage testing is performed between different data sources. Subsystems in overly sparse subsets are removed. In the same dataset, data from systems such as power and machinery may be missing due to factors such as damage to the data acquisition equipment within the plant. For example, if there is little data on the power system within a plant, it may not be of reference value. Therefore, the power subsystem data in that subset is removed.

[0038] S2. Prior rule knowledge acquisition: Using the associated features collected from actual samples as keywords, literature is collected and mined to form a literature set. Based on the literature set, relationships are extracted through natural language processing and entity recognition methods, and a prior knowledge base is formed with keywords as the core.

[0039] In S2, after collecting and mining the literature, a comprehensive evaluation index is constructed based on the journal in which the literature is published, the number of citations, and the author's institution. Based on this, the literature is sorted, and the literature with the lowest ranking is removed to form a literature collection.

[0040] Related features, such as "fault detection", "early warning", "voltage", "current", "vibration" and "doubly fed wind turbine" (which are related to the faults of doubly fed generators), were used as keywords for literature collection and mining.

[0041] In the process of literature collection and mining, a comprehensive evaluation index is constructed based on the journal in which the literature is published, the number of citations, and the author's institution. Based on this, the literature is ranked and the literature with the lowest ranking is removed to form a literature collection.

[0042] For the sorted literature set, relationships are extracted using natural language processing and entity recognition methods. A framework-based prior knowledge base is formed with keywords such as "fault detection", "early warning", "voltage", "current", "vibration" and "doubly fed wind turbine" as the core.

[0043] S3, multi-source data and rule transfer learning, for each sample dataset, builds a model based on within-group data, using features as nodes and relationships between samples as edges, forming a network of relationships between features, i.e., a sample relationship network.

[0044] Based on a prior knowledge base and a corresponding sample relationship network, a prior knowledge network is constructed, i.e., a specific network is created.

[0045] Based on sample relationship networks and prior knowledge bases, different complex networks are built using different data sources, forming several sub-networks with features as nodes and relationships as edges.

[0046] For the several sub-network sets formed, a similar network fusion method is used to fuse the networks, resulting in a complex network containing different network features and fault relationships at different levels, which serves as the basic dataset for wind turbine fault detection.

[0047] In S3, the sample relationship network is represented as G. similarity = (V, E), where node V corresponds to the data at each time point, and edge E corresponds to the similarity weight between samples. Sample similarity is represented by an n×n similarity matrix W, where W(i,j) represents the similarity between samples. The prior knowledge network is G. prior = (V,E′), where edge E′ corresponds to the similarity weight between samples. The sample similarity is represented by an n×n similarity matrix W″, W″(i,j)=(1-α)·W(i,j)+α·W′(i,j), where α is the weighting coefficient, and W′(i,j) is obtained by multiplying the first weight matrix formed by the frequency of rule occurrence in the prior knowledge base in S2 and the second weight matrix formed by the rule weights in the expert weight base.

[0048] (1) For each sample dataset, i.e., the data collected at the same time is called a sample), based on the data within the group, the model is built with features, i.e. variables, as nodes and the relationship between samples as edges, forming a network of relationships between features, i.e., the sample relationship network.

[0049] Specifically, assuming there are m operational data points and n measured values ​​(such as corresponding voltage, current, vibration, etc.), the sample similarity network is represented as G. similarity = (V, E).

[0050] In this network, nodes V correspond to the data at each time point, edges E correspond to the similarity weights between samples, and sample similarity is represented by an n×n similarity matrix W, where W(i,j) represents the similarity between samples. Sample similarity can be calculated using Euclidean distance or mutual information of the sample data.

[0051] Based on the above calculation of sample correlation, a sample relationship network is formed.

[0052] (2) Based on the prior database in S2 and combined with the sample relationship network in (1), a prior knowledge network G is constructed. prior = (V, E′), that is, constructing a specific network G = {G similarity G prior}

[0053] The prior knowledge network is similar to the sample relationship network, except that edge E' corresponds to the similarity weight between samples. Sample similarity is represented by an n×n similarity matrix W″, W″(i,j)=(1-α)·W(i,j)+α·W′(i,j). α is a weighting coefficient used to reflect the importance of prior knowledge weights for sample association. The value of α needs to be optimized and adjusted during the classification training process based on the actual situation.

[0054] W′(i,j) is obtained by multiplying the first weight matrix formed by the frequency of rule occurrences in the prior knowledge base of S2, and the second weight matrix formed by the weights of rules in the expert weight base. A higher frequency of occurrence indicates a higher reliability of the rule; the same logic applies to the weights of rules in the expert weight base. The expert weight base can be formed through expert questionnaires. For domains where experts are scarce, the first weight matrix can also be directly used as W′(i,j).

[0055] In this way, based on the sample relationship network and prior knowledge base, the interrelationships between all feature variables can be obtained.

[0056] (3) Based on the sample relationship network obtained in (1) and the prior knowledge base in s2, different complex networks can be established based on different data sources, and with features as nodes and relationships as edges, several sub-networks are finally formed.

[0057] (4) For the sub-network set in (3), the Similarity Network Fusion (SNF) method is used to perform network fusion to obtain a complex network containing different network features and different levels of fault relationships, which serves as the basic dataset for wind turbine fault detection.

[0058] The specific steps are as follows:

[0059] After completing the construction of the specific network and obtaining multiple subnetworks to be fused, a fully sparse kernel function, namely a normalized weight matrix P = D, is defined on the vertex set V to compute the fusion matrix from various types of measurements. -1 W, where D is a diagonal matrix, and the diagonal elements D(i,i) = ∑ j W(i,j), where W is the similarity matrix mentioned in network construction. Since matrix P is a diagonal matrix, then Σ j p(i,j) = 1. To address the impact of sample numerical instability on normalization (related to self-similarity on the matrix diagonal), the weight matrix is ​​normalized using the following method, which is unaffected by autocorrelation of diagonal elements:

[0060]

[0061] Then, the local affinity s(i,j) is measured using the K-nearest neighbor method, assuming N i The sample similarity network G contains x i Given a series of adjacent samples, s(i,j) is calculated as follows:

[0062]

[0063] This operation sets the similarity points between non-adjacent objects (based on pairwise similarity values) to zero.

[0064] Matrix P contains all the information about the similarity of each sample to all other samples, while matrix S only encodes the similarity of each sample to its K most similar samples. During the fusion process, our algorithm always starts with P as the initial state and S as the kernel matrix, which captures the local structure of the graph while improving computational efficiency.

[0065] Given m different types of data, a similarity matrix W can be constructed using (1) and (2). (v) Where v = 1, 2, ..., m represents different sub-network views constructed from different data. Then, P is calculated using formulas 4 and 5 respectively. (v) S (v) Finally, the iterative fusion of the subnetworks is completed.

[0066] First, taking the fusion of the simplest two-class data subnetworks with m=2 as an example, the steps of the SNF fusion algorithm are explained. The state matrix P is calculated from the two input similarity matrices. (1) and P (2) As shown in Formula 4; then the kernel matrix S is obtained. (1) and S (2) As shown in Formula 5. Let Representing the initial state matrix at time t=0, a key step in SNF is to iteratively update the similarity matrix corresponding to each data type, as shown below:

[0067]

[0068]

[0069] in, It is the state matrix of the first data type after t iterations. This is the state matrix of the second data type after t iterations. Each iteration updates the state matrix, generating two parallel exchange-diffusion processes. After t steps, the overall state matrix is ​​updated as follows:

[0070]

[0071] Since matrix S is a K-nearest neighbor graph of P, it can reduce noise between instances, thus SNF is robust to noise in similarity metrics. After each iteration, for and Perform normalization, as shown in Equation 4. By performing normalization, we can ensure that during the SNF iteration process, the patient's sample data is always most similar to its own data rather than that of other patients; this ensures that the final network is full-rank, which is crucial for the final network's classification and clustering applications. Finally, using this normalization method can accelerate the convergence speed of SNF. Finally, extending the data type to the case where m > 2, the updated state matrix is ​​as follows:

[0072]

[0073] Following S3, data supplementation is performed. For the same dataset, statistical analysis of data volume, positive and negative examples, and features is conducted, along with balance detection. For datasets with significantly fewer data points and fault types with poor balance, data supplementation is performed based on the simulation model. During the data supplementation process, the data is gradually increased by 10%, 20%, 30%, up to 100%, and statistical analysis is performed. At the same time, the significance of features and the correlation between features are monitored. When the deviation exceeds 5%, the supplementation of simulation data is stopped.

[0074] For datasets with significantly smaller sample sizes (which could be the bottom 5%, 10%, 20%, or 30% depending on the specific dataset) and fault types with poor balance (which could be the bottom 5%, 10%, 20%, or 30% of faults with a good balance between positive and negative examples), data supplementation is performed based on the simulation model. Since data supplementation is independent of the model learning process, it is not limited to S3 and can be performed concurrently with S1.

[0075] S4. Feature group model partitioning: Community detection is performed on the fused model. Hierarchical clustering, elbow statistics, or silhouette coefficient method are used to optimize the number of cluster centers to obtain the final number of cluster centers. Based on this clustering result, the grouping relationship of features is determined, thereby realizing the grouping of features.

[0076] like Figure 2 As shown, S5, the multi-classification model is built based on the above feature grouping results. A two-level mapping model is set up. Within each community, a preliminary mapping model is established. The mapping model can be obtained from: support vector regression, BP network, extreme learning machine, deep neural network, and similar machine learning classification algorithms. Each community combination (i.e., features) 1.1 To characteristics 1.k The combined feature values ​​(i.e., feature combination 1) are formed. Using these combined feature values ​​as input, a higher-level mapping model is further built. The higher-level mapping model can be obtained by support vector regression, BP network, extreme learning machine, deep neural network and similar machine learning classification algorithms. After training, multi-classification results of faults can be obtained, forming a motor fault transfer diagnosis model. The data in the process is input into the motor fault transfer diagnosis model to diagnose and predict faults.

[0077] like Figure 3 As shown, after step S5, system verification is performed. Based on the motor fault migration diagnosis model in S5, motor faults are diagnosed. A simulation incremental model is built using actual data based on the steps in S5 to diagnose motor faults. When the difference between the motor fault migration diagnosis model and the simulation incremental model is greater than 5%, the actual data is added to the basic dataset to update the basic dataset, and the new basic dataset is used to update the motor fault migration diagnosis model.

[0078] like Figure 3 As shown, the motor fault migration diagnosis model obtained in S5 is used as the online operation model to diagnose motor faults.

[0079] Based on actual data from the actual production process, another motor fault migration diagnosis model, namely the simulation incremental model, is trained using the steps in S5. The motor fault is then diagnosed based on the simulation incremental model.

[0080] A difference detection is performed between the online running model and the simulation incremental model to see if the difference is acceptable. If the difference is less than or equal to 5%, it is considered acceptable, and the online running model is not updated. If it is greater than 5%, it is unacceptable, and the actual data is added to the basic dataset to form a new basic dataset. A new motor fault transfer diagnosis model is trained using the new basic dataset.

[0081] At a fixed interval (ideally between one week and one month, and more frequently in the early stages of system operation), when the difference between the online running model system and the simulation incremental system exceeds 5%, update the base dataset with actual data. Then, rebuild the new simulation recognition system and repeat the comparison process.

Claims

1. A method for fault diagnosis of a doubly-fed generator using multi-source data and transfer learning, characterized in that, Includes the following steps: S1. Multi-source data collection and preprocessing: Collect operational data from different data sources and preprocess the operational data from each data source. S2. Prior rule knowledge acquisition: Using the associated features collected from actual samples as keywords, literature is collected and mined to form a literature set. Based on the literature set, relationships are extracted through natural language processing and entity recognition methods, and a prior knowledge base is formed with keywords as the core. S3, multi-source data and rule transfer learning, for each sample dataset, builds a model based on within-group data, using features as nodes and relationships between samples as edges, forming a network of relationships between features, i.e., a sample relationship network. Based on a prior knowledge base and a corresponding sample relationship network, a prior knowledge network is constructed, i.e., a specific network is created. Based on sample relationship networks and prior knowledge bases, different complex networks are built using different data sources, forming several sub-networks with features as nodes and relationships as edges. For the several sub-network sets formed, a similar network fusion method is used to fuse the networks and obtain a complex network containing different network features and different levels of fault relationships, which serves as the basic dataset for wind turbine fault detection. S4. Feature group model partitioning: Community detection is performed on the fused model. Hierarchical clustering, elbow statistics, or silhouette coefficient method are used to optimize the number of cluster centers to obtain the final number of cluster centers. Based on this clustering result, the grouping relationship of features is determined, thereby realizing the grouping of features. S5. Multi-classification model construction: Based on the above feature grouping results, a two-level mapping model is set up. In each community, a preliminary mapping model is established. Each community combination forms a combined feature value. Using such combined feature values ​​as input, a higher-level mapping model is further built. After training, multi-classification results of faults can be obtained, forming a motor fault migration diagnosis model. The data in the process is input into the motor fault migration diagnosis model to diagnose and predict faults.

2. The method for fault diagnosis of a doubly-fed generator based on multi-source data and transfer learning according to claim 1, characterized in that: In the multi-source data collection and preprocessing, data cleaning is performed on each subset of data, i.e., the data within a single data source, to remove features that cover less than 70% of the sample size. Samples with less than 70% coverage of features are removed. Coverage detection is not performed between different data sources, and subsystems in overly sparse subsets are eliminated.

3. The method for fault diagnosis of a doubly-fed generator based on multi-source data and transfer learning according to claim 1, characterized in that: In S2, after collecting and mining the literature, a comprehensive evaluation index is constructed based on the journal in which the literature is published, the number of citations, and the author's institution. Based on this, the literature is sorted, and the literature with the lowest ranking is removed to form a literature collection.

4. The method for fault diagnosis of a doubly-fed generator based on multi-source data and transfer learning according to claim 1, characterized in that: Following S3, data supplementation is performed. For the same dataset, statistical analysis of data volume, positive and negative examples, and features is conducted, along with balance detection. For datasets with significantly fewer data points and fault types with poor balance, data supplementation is performed based on the simulation model. During the data supplementation process, the data is gradually increased by 10%, 20%, 30%, up to 100%, and statistical analysis is performed. At the same time, the significance of features and the correlation between features are monitored. When the deviation exceeds 5%, the supplementation of simulation data is stopped.

5. The method for fault diagnosis of a doubly-fed generator based on multi-source data and transfer learning according to claim 1, characterized in that: Following S5, system verification is performed. Based on the motor fault migration diagnosis model in S5, motor faults are diagnosed. A simulation incremental model is built using actual data based on the steps in S5 to diagnose motor faults. When the difference between the motor fault migration diagnosis model and the simulation incremental model is greater than 5%, the actual data is added to the basic dataset to update the basic dataset, and the new basic dataset is used to update the motor fault migration diagnosis model.

6. The method for fault diagnosis of a doubly-fed generator using multi-source data and transfer learning according to claim 1, characterized in that: The preprocessing in S1 includes normalization of the data within the dataset and outlier removal.

7. The method for fault diagnosis of a doubly-fed generator using multi-source data and transfer learning according to claim 1, characterized in that: In S3, the sample relationship network is represented as follows: ,node For each time point, the edge The similarity weights between corresponding samples are calculated by... Similarity matrix Characterization, To represent the similarity between samples, the prior knowledge network is... ,side The similarity weights between corresponding samples are calculated by... Similarity matrix Characterization, , These are weighting coefficients. It is obtained by multiplying the first weight matrix formed by the frequency of rule occurrence in the prior knowledge base in S2 and the second weight matrix formed by the rule weights in the expert weight base.