Multi-source heterogeneous data privacy protection fusion processing method for edge computing nodes

Abstract

The application discloses a multi-source heterogeneous data privacy protection fusion processing method for edge computing nodes, relates to the field of edge computing, and comprises the following steps: step 1: obtaining multi-source heterogeneous original data distributed in multiple edge computing nodes, and generating an encrypted data set carrying an attribute label tree index; step 2: taking the encrypted data set carrying the attribute label tree index as input, and generating a reduced encrypted data set; step 3: grouping and decrypting the reduced encrypted data set according to the edge computing node attribution, and outputting a global joint distribution value as a joint probability representation of the fused multi-source heterogeneous data. The application realizes efficient dimension reduction and joint probability fusion of multi-source heterogeneous data under the premise of protecting data privacy.

Description

Technical Field

[0001] This invention relates to the field of edge computing, and in particular to a method for privacy protection and fusion processing of multi-source heterogeneous data for edge computing nodes. Background Technology

[0002] Existing multi-source data fusion methods mainly fall into two categories: feature-level fusion and decision-level fusion. Feature-level fusion methods typically map data from different sources to a unified feature space and then concatenate or weighted the data. Typical techniques include principal component analysis, autoencoders, and multi-view learning. These methods perform well when dealing with homogeneous data, but when faced with heterogeneous data such as numerical, textual, and sequential data, the differences in scale, representation, and statistical properties between different data types make unified mapping of the feature space difficult. Simple concatenation or weighting methods cannot accurately characterize the nonlinear dependencies between heterogeneous attributes. Decision-level fusion methods, on the other hand, perform voting, averaging, or Bayesian combination of the output results after independent modeling of each data source. While this avoids the problem of heterogeneous feature alignment, it loses the fine-grained correlation information of underlying attributes between data sources, and the fusion effect is limited by the performance upper bound of each independent model.

[0003] In terms of data privacy protection, multi-source data fusion in edge computing scenarios faces severe privacy leakage risks. Data collected by each edge computing node often contains sensitive information such as device status, production parameters, or user behavior. Directly uploading the raw data to the central server for fusion processing may lead to privacy leaks. Existing privacy protection technologies mainly include differential privacy, homomorphic encryption, and secure multi-party computation. Differential privacy protects the privacy of individual records by adding noise to the data, but the introduction of noise inevitably reduces the statistical accuracy of the data, limiting its application in industrial scenarios with high fusion accuracy requirements. Fully homomorphic encryption theoretically supports arbitrary computation on ciphertext, but its computational overhead is extremely high, making practical deployment difficult under the limited computing power of edge computing nodes. Secure multi-party computation requires extensive interactive communication between multiple participants, resulting in excessively high communication costs in scenarios with a large number of edge computing nodes and limited network bandwidth. None of the above privacy protection methods fully consider the differences in privacy requirements at each stage of the multi-source heterogeneous data fusion process, lacking a hierarchical privacy protection mechanism for different stages such as data encoding, attribute filtering, and dependency modeling. Summary of the Invention

[0004] The purpose of this invention is to provide a privacy-preserving fusion processing method for multi-source heterogeneous data oriented to edge computing nodes, which achieves efficient dimensionality reduction and joint probability fusion of multi-source heterogeneous data while protecting data privacy.

[0005] To address the aforementioned technical problems, this invention provides a method for privacy-preserving fusion processing of multi-source heterogeneous data for edge computing nodes, comprising the following steps: Step 1: Obtain multi-source heterogeneous raw data distributed across multiple edge computing nodes, uniformly encode the multi-source heterogeneous raw data based on a preset discretized dictionary, construct an attribute label tree index structure, generate a node master key for each edge computing node, and perform searchable encryption processing based on the node master key to generate an encrypted dataset carrying the attribute label tree index. Step 2: Taking the encrypted dataset with attribute label tree index as input, construct indistinguishable relations on the set of conditional attributes based on the index labels and divide them into equivalence classes, construct the conditional attribute discrimination matrix, perform attribute reduction operation without decrypting the attribute ciphertext data, and generate a reduced encrypted dataset. Step 3: Group and decrypt the reduced encrypted dataset according to the edge computing node affiliation, perform edge distribution transformation processing, determine the Gumbel family dependency parameters based on Kendall rank correlation coefficient, construct nested Copula structures within nodes and cross-node Copula dependency structures to form a hierarchical nested Copula fusion model, perform data fusion operation through the hierarchical nested Copula fusion model, and output the global joint distribution value as the joint probability representation of the fused multi-source heterogeneous data.

[0006] Furthermore, the multi-source heterogeneous raw data includes numerical sensor data, text log data, and sequential state data; the pre-defined discretization dictionary includes a binning boundary table for numerical sensor data, a vocabulary mapping table for text log data, and time granularity parameters for sequential state data, and the pre-defined discretization dictionary is synchronized across all edge computing nodes; the unified encoding process is as follows: the numerical sensor data is discretized and binned according to the binning boundary table to obtain numerical interval numbers; the text log data is segmented and mapped according to the vocabulary mapping table to obtain vocabulary index numbers; and the sequential state data is sliced ​​according to the time granularity parameters to obtain time period index numbers.

[0007] Furthermore, the construction process of the attribute tag tree index structure is as follows: a root node is created as the data source identifier node, and three level 1 child nodes are created under the root node to correspond to the three data types: numerical sensor data, text log data, and sequence status data. Under each level 1 child node, a corresponding number of level 2 leaf nodes are created according to the number of attributes contained in the corresponding data type. Each level 2 leaf node is associated with the number value range of the corresponding attribute.

[0008] Furthermore, the searchable encryption process includes two sub-processes: index tag generation and data encryption. The index tag generation sub-process is as follows: for each second-level leaf node in the attribute tag tree index structure, the path code from the root node to the corresponding second-level leaf node is extracted. The path code, the range of the number associated with the second-level leaf node, and the current synchronization cycle identifier are used as inputs, and the node master key is used as the key to call a pseudo-random function to generate an index tag. The data encryption sub-process is as follows: the node master key and the path codes of each second-level leaf node are used as inputs to call a key derivation function to generate an attribute encryption key. A random initial vector is generated for each data record. The attribute encryption key and the random initial vector are used to symmetrically encrypt the encoded data of each attribute in the data record to obtain attribute ciphertext data. The attribute ciphertext data is then associated with and stored with the index tag of the corresponding second-level leaf node.

[0009] Furthermore, in step 2, a query token is constructed to locate the target attribute without decrypting the attribute ciphertext data. The process of constructing the query token is as follows: using the node master key as the key, and the path code, number value range, and current synchronization cycle identifier of the target attribute as inputs, a pseudo-random function is called to generate the query token. The second-level leaf node corresponding to the target attribute is located by comparing the matching relationship between the query token and the index label. The process of constructing the indistinguishability relationship is as follows: for any two encrypted data records in the encrypted dataset carrying the attribute label tree index, each attribute in the condition attribute set is traversed. The indistinguishability is determined by comparing whether the index labels of the two encrypted data records on the corresponding attribute are the same. If all the index labels of the two encrypted data records on a certain attribute subset of the condition attribute set are the same, then the two encrypted data records are determined to be indistinguishable with respect to the corresponding attribute subset. Based on the indistinguishability relationship, the encrypted dataset carrying the attribute label tree index is divided into several equivalence classes.

[0010] Furthermore, the construction process of the conditional attribute resolution matrix is ​​as follows: Create a square matrix with the number of rows and columns equal to the number of equivalence classes. For any two distinct equivalence classes, iterate through each attribute in the conditional attribute set. If the index labels of the representative records of the two equivalence classes on the corresponding attributes are different, then fill the corresponding attribute identifiers into the cells corresponding to the two equivalence classes in the conditional attribute resolution matrix. Store the conditional attribute resolution matrix in a sparse matrix format. The attribute reduction operation is performed as follows: Count the frequency of each attribute identifier in all non-empty cells, and remove attribute identifiers with a frequency of zero from the conditional attribute set. In addition to obtaining the candidate attribute set, the reduced attribute set is initialized to an empty set. Iteratively, the attribute identifier that appears most frequently in the uncovered non-empty cells is selected from the candidate attribute set and added to the reduced attribute set. Non-empty cells containing the corresponding attribute identifier are marked as covered. This iteration is repeated until all non-empty cells are covered. Based on the reduced attribute set, attribute projection is performed on the encrypted dataset carrying the attribute label tree index. The attribute ciphertext data and index labels corresponding to the attribute identifiers in the reduced attribute set are retained, and the attribute ciphertext data and index labels corresponding to other attribute identifiers are removed to generate the reduced encrypted dataset.

[0011] Furthermore, in step 3, the reduced encrypted dataset is grouped according to the edge computing node affiliation to obtain multiple edge node reduced encrypted data subsets. A global object identifier is assigned to each data record. The global object identifier consists of the data acquisition time window index and the business object code. For each edge computing node, the attribute ciphertext data in the edge node reduced encrypted data subset is decrypted using the corresponding node master key to obtain the edge node reduced plaintext data subset. The execution process of the edge distribution transformation is as follows: for each attribute in the reduced attribute set, all values ​​of the corresponding attribute in the edge node reduced plaintext data subset are extracted to form an attribute value sequence. The attribute value sequence is sorted in ascending order and a rank is assigned to each attribute value. The rank of each attribute value is divided by the length of the attribute value sequence and 1 is added to obtain the edge probability integral transformation value. All values ​​of the corresponding attribute are converted into an edge probability integral transformation value sequence located in the open interval between 0 and 1.

[0012] Furthermore, the calculation process of the Kendall rank correlation coefficient is as follows: For any two attributes, the marginal probability integral transformation value sequences are paired to form a data pair set. For any two data pairs in the data pair set, if the difference between the two component values ​​of the first data pair and the two component values ​​of the second data pair has the same sign, they are determined to be a consistent pair; otherwise, they are determined to be a non-consistent pair. The difference between the number of consistent pairs and the number of non-consistent pairs is divided by the total number of pairwise combinations to obtain the Kendall rank correlation coefficient. Based on the Kendall rank correlation coefficients of all attribute pairs, an intra-node Kendall rank correlation matrix is ​​constructed. The process of determining the Gumbel family dependency parameters is as follows: The Kendall rank correlation coefficient value is converted into a Gumbel family dependency parameter using the parameter inversion relation of the Gumbel family Copula. The Gumbel family dependency parameter is equal to 1 divided by 1 minus the absolute value of the Kendall rank correlation coefficient value. When the Kendall rank correlation coefficient value is negative, a negative correlation label is added to the converted Gumbel family dependency parameter.

[0013] Furthermore, the construction process of the nested Copula structure within a node is as follows: the attributes in the reduced attribute set are hierarchically clustered according to the magnitude of the Gumbel family dependency parameters between attribute pairs. Attribute pairs with larger Gumbel family dependency parameters are preferentially aggregated to form bottom-level subgroups. Each bottom-level subgroup is then aggregated according to the average Gumbel family dependency parameter between subgroups to form upper-level groups. This aggregation is repeated layer by layer until all attributes are grouped into the same top-level group to form a tree-like nested structure. The construction process of the cross-node Copula dependency structure is as follows: for any two edge computing nodes, the Frobenius distance between the intra-node Kendall rank correlation matrices of the two edge computing nodes is calculated. The quotient obtained by subtracting the Frobenius distance from 1 and dividing it by the square root of the matrix dimension is used as the node similarity coefficient. The node similarity coefficient is converted into cross-node Gumbel family dependency parameters through the Gumbel family parameter inversion relationship. A cross-node dependency parameter matrix is ​​constructed based on the cross-node Gumbel family dependency parameters of all edge computing node pairs.

[0014] Furthermore, the layered nested Copula fusion model has a bottom layer consisting of nested Copula structures within each edge computing node, and a top layer consisting of a cross-node nested Copula structure built based on the cross-node dependency parameter matrix. The data fusion operation is performed as follows: data records of each edge computing node are aligned according to the global object identifier, and data records with the same global object identifier are grouped into the same fusion group. For each fusion group, the joint distribution function value of the Gumbel family Copula is first calculated layer by layer from the bottom subgroup to the top group within each edge computing node according to the nested Copula structure within each node. During each layer's calculation, the joint distribution function value output by the lower layer is used as input and combined with the Gumbel family dependency parameters of the corresponding layer to calculate the joint distribution function value of the corresponding layer, thus obtaining the joint distribution value within each edge computing node. Then, the global joint distribution value is calculated according to the cross-node nested Copula structure, using the joint distribution value within each edge computing node as input and combining it with the cross-node Gumbel family dependency parameters.

[0015] The privacy-preserving fusion processing method for multi-source heterogeneous data oriented towards edge computing nodes proposed in this invention has the following beneficial effects: This method organically links three technical steps—searchable encryption, rough set attribute reduction, and hierarchical nested Copula dependency modeling—to achieve a balance between privacy protection and efficient processing throughout the entire data fusion process. In the data encoding and encryption stage, this invention uses a pre-defined discretized dictionary to uniformly encode numerical sensor data, text-based log data, and sequential state data into discretized numbers, eliminating differences in dimensions and representation forms between heterogeneous data. Furthermore, it implements searchable encryption processing based on an attribute label tree index structure and a pseudo-random function, enabling subsequent attribute reduction operations to be completed directly in the ciphertext domain through index label comparison. This allows for the determination of indistinguishable relationships between data records without decrypting the original data, fundamentally avoiding the risk of privacy leakage during attribute reduction. In the attribute reduction stage, this invention constructs a conditional attribute discrimination matrix and employs a frequency-based greedy covering strategy to remove redundant attributes while maintaining the distinguishing ability of equivalence classes. This significantly reduces the data dimensionality and computational overhead of subsequent fusion calculations. Simultaneously, the sparse matrix storage format effectively reduces the memory footprint of the discrimination matrix. In the data fusion stage, this invention combines marginal distribution transformation based on Kendall's rank correlation coefficient with Gumbel family Copula dependency modeling. The original values ​​of each attribute are mapped to a unified probability space through probability integral transformation before dependency analysis. This eliminates the limitations of parameter assumptions regarding variable distribution patterns and accurately characterizes nonlinear monotonic dependencies. The nested Copula structure within nodes organizes attribute pairs with different dependency strengths hierarchically through hierarchical clustering. The cross-node Copula dependency structure measures the distribution differences between nodes using Frobenius distance and converts them into cross-node dependency parameters. The hierarchical nested Copula fusion model composed of these two structures can simultaneously capture fine-grained associations between attributes within nodes and coarse-grained spatial associations between nodes. The output global joint distribution value provides a unified joint probability representation for multi-source heterogeneous data, which can be directly used for downstream tasks such as anomaly detection and situation assessment, and has strong engineering practical value. Attached Figure Description

[0016] Figure 1 This is a schematic diagram illustrating the principle of determining consistent and non-consistent pairs in the Kendall rank correlation coefficient calculation process provided in this embodiment of the invention. Figure 2 A schematic diagram of the contour distribution of the Gumbel family Copula joint distribution function on a two-dimensional unit plane when the Gumbel family dependency parameters are set to 1.2 and 2.0, respectively, according to an embodiment of the present invention. Figure 3The diagram shows the contour lines of the joint distribution function of the Gumbel family Copula on a two-dimensional unit plane when the Gumbel family dependency parameters are set to 3.5 and 6.0, respectively, according to the embodiments of the present invention. Detailed Implementation

[0017] A privacy-preserving fusion processing method for multi-source heterogeneous data in edge computing nodes includes the following steps: Step 1: Obtain multi-source heterogeneous raw data distributed across multiple edge computing nodes, uniformly encode the multi-source heterogeneous raw data based on a preset discretized dictionary, construct an attribute label tree index structure, generate a node master key for each edge computing node, and perform searchable encryption processing based on the node master key to generate an encrypted dataset carrying the attribute label tree index. Step 2: Taking the encrypted dataset with attribute label tree index as input, construct indistinguishable relations on the set of conditional attributes based on the index labels and divide them into equivalence classes, construct the conditional attribute discrimination matrix, perform attribute reduction operation without decrypting the attribute ciphertext data, and generate a reduced encrypted dataset. Step 3: Group and decrypt the reduced encrypted dataset according to the edge computing node affiliation, perform edge distribution transformation processing, determine the Gumbel family dependency parameters based on Kendall rank correlation coefficient, construct nested Copula structures within nodes and cross-node Copula dependency structures to form a hierarchical nested Copula fusion model, perform data fusion operation through the hierarchical nested Copula fusion model, and output the global joint distribution value as the joint probability representation of the fused multi-source heterogeneous data.

[0018] In real-world edge computing scenarios, multiple edge computing nodes each undertake different types of data acquisition tasks. Taking the Industrial Internet of Things (IIoT) as an example, in a smart factory deploying eight edge computing nodes, the data collected by different nodes differs significantly in type and format. The multi-source heterogeneous raw data includes numerical sensor data, text-based log data, and sequential status data. Numerical sensor data comes from physical quantity acquisition devices such as temperature sensors, vibration sensors, and pressure sensors, and its raw form is continuous floating-point values, such as a temperature of 28.35 degrees Celsius or a vibration acceleration of 0.782g. Text-based log data comes from information sources such as equipment operation logs and fault alarm records, containing text content that mixes natural language descriptions and structured code. Sequential status data is a time series formed by the changes in the operating status of equipment over time, such as the start-stop state transition sequence of a motor or the trajectory of valve opening / closing changes.

[0019] Because the three types of data mentioned above differ significantly in data format, value range, and semantic dimension, directly performing subsequent encryption and attribute reduction operations on the original data will face difficulties in data alignment and comparison. To solve this problem, this method synchronously pre-defines a discretization dictionary across all edge computing nodes, using unified encoding to convert different types of original data into discretized representations within the same numbering space. The pre-definement dictionary includes a binning boundary table for numerical sensor data, a vocabulary mapping table for text-based log data, and time granularity parameters for sequence-based state data.

[0020] Binning boundary tables are used to divide continuous numerical sensor data into a finite number of discrete intervals. Taking temperature sensing attributes as an example, assuming the actual acquisition range is 0 to 100 degrees Celsius, the binning boundary table divides this range into several intervals according to an equal-width or equal-frequency strategy. If an equal-width binning strategy is adopted and the bin width is set to 5 degrees Celsius, 20 bin intervals are generated, corresponding to numerical interval numbers 1 to 20. An original temperature value of 28.35 degrees Celsius falls into the 6th bin interval (25 to 30 degrees Celsius), and is therefore encoded as numerical interval number 6. In another optional implementation, an equal-frequency binning strategy can also be used, that is, based on the distribution of historical data, the number of samples in each bin is approximately equal. This method can provide higher discrimination when the data distribution is uneven.

[0021] A vocabulary mapping table is used to convert text-based log data into numerical identifiers. The vocabulary mapping table is constructed based on the historical log corpus of all edge computing nodes. After word segmentation, high-frequency words are extracted, sorted in descending order of frequency, and assigned word index numbers sequentially. Assuming the vocabulary mapping table contains 5000 entries, each entry corresponds to a word index number from 1 to 5000. When performing word segmentation and mapping on a piece of text-based log data, the log text is split into a sequence of words, and each word is replaced with its corresponding word index number from the vocabulary mapping table. Low-frequency words not appearing in the vocabulary mapping table are uniformly mapped to number 0 as unknown word markers.

[0022] The time granularity parameter is used to slice sequential state data along the time axis. The time granularity parameter specifies the length of the time window for each slice, for example, set to 30 seconds. A 10-minute sequence of device states will be divided into 20 time periods, each corresponding to a time period index number. Within each time period, the characteristics of the state sequence are represented by compressed statistics, for example, taking the most frequently occurring state value within that time period as the representative state code for that time period. In an optional implementation, the time granularity parameter can also be set to other values ​​depending on the specific application scenario; for example, it can be set to 10 seconds for high-frequency sampled vibration state sequences, and 60 seconds for slowly changing environmental monitoring state sequences.

[0023] After the unified encoding is completed, each attribute value in each data record is converted into a corresponding number representation. Regardless of whether its original type is numerical sensor data, text log data, or sequence status data, it participates in subsequent processing in a unified number format.

[0024] An attribute label tree index structure is constructed based on unified encoding to organize and index the encoded data of each attribute. The attribute label tree index structure adopts a three-level tree topology. A root node is created at the top level as the data source identifier node, carrying the global identifier information of the current edge computing node. Three level-1 child nodes are created under the root node, corresponding to three data types: numerical sensor data, text log data, and sequence status data. Each level-1 child node represents the classification of a data type. Under each level-1 child node, a corresponding number of level-2 leaf nodes are created based on the number of attributes contained in the corresponding data type. For example, in a specific implementation scenario, numerical sensor data includes three attributes: temperature, vibration, and pressure; therefore, three level-2 leaf nodes are created under the level-1 child node corresponding to numerical sensor data. Text log data includes two attributes: fault description and operation record; therefore, two level-2 leaf nodes are created under the level-1 child node corresponding to text log data. Sequence status data includes two attributes: running status and load status; therefore, two level-2 leaf nodes are created under the level-1 child node corresponding to sequence status data. Each level 2 leaf node is associated with the range of values ​​for its corresponding attribute, that is, all possible ranges of numbers that the attribute can take after unified coding. Taking the temperature attribute as an example, if 20 range numbers are generated after binning, then the range of values ​​for the numbers associated with the level 2 leaf nodes of the temperature attribute is from 1 to 20.

[0025] The tree-like organization of the attribute tag tree index structure ensures that each second-level leaf node has a unique path from the root node to itself. This path encodes information at three levels: data source identifier, data type, and specific attribute. This hierarchical path encoding plays a crucial role in subsequent searchable encryption processing and attribute reduction operations.

[0026] After constructing the attribute label tree index structure, a node master key is generated for each edge computing node, and searchable encryption is performed based on the node master key. The node master key is a 256-bit random bit string generated by a cryptographically secure random number generator. Each edge computing node holds its own independent node master key, and the node master keys of different nodes are different, thus ensuring the isolation of encrypted data from each node.

[0027] The searchable encryption process comprises two sub-processes: index tag generation and data encryption. The goal of the index tag generation sub-process is to generate a cryptographic index tag for each second-level leaf node in the attribute tag tree index structure, allowing authorized parties to locate and match attributes using the index tags without accessing the plaintext data. For each second-level leaf node, the path code from the root node to the corresponding second-level leaf node is first extracted. Taking the temperature attribute as an example, assuming the root node code is "N01", the first-level child node code corresponding to the numerical sensor data is "T1", and the second-level leaf node code corresponding to the temperature attribute is "A01", then the path code is the concatenation of these three codes. Using the path code, the range of numbers associated with the second-level leaf nodes, and the current synchronization cycle identifier as input, a pseudo-random function is invoked using the node master key to generate index tags. The current synchronization cycle identifier is a counter value that increments with the data synchronization cycle. Its purpose is to ensure that even the same attribute will generate different index tags in different synchronization cycles, thus preventing attackers from inferring the attribute correspondence by comparing index tags from different periods. Let the pseudo-random function be... The node master key is Path encoding is The range of the number values ​​is The current synchronization period is identified as Then the index label The calculation process is as follows ,in This represents the bit string concatenation operation. In one alternative implementation, the pseudo-random function can be constructed based on HMAC-SHA256 or AES, as long as it satisfies the pseudo-randomness requirement.

[0028] The data encryption sub-process is responsible for encrypting and protecting the actual encoded data. It takes the node master key and the path codes of each second-level leaf node as input and calls the key derivation function to generate the attribute encryption key. The key derivation function uses... Path encoding of each level 2 leaf node As input, the output is the attribute encryption key, i.e. ,in This represents the key derivation function. The key derivation function generates an independent attribute encryption key for each attribute. Different attributes are encrypted using different attribute encryption keys, so even if the encryption key of one attribute is leaked, the security of other attributes will not be affected. In an optional implementation, the key derivation function can be implemented using HKDF (HMAC-based key derivation function).

[0029] For each data record, a random initialization vector is generated. The length of the random initialization vector matches the symmetric encryption algorithm used; for example, if AES-256-CBC mode is used, the random initialization vector length is 128 bits. The encoded data of each attribute in the data record is symmetrically encrypted using the attribute encryption key and the random initialization vector to obtain the attribute ciphertext data. Let... Represents a symmetric encryption function. Represents a random initial vector. If the data is encoded, then the attribute ciphertext data is... for Each attribute in each data record is independently encrypted using its corresponding attribute encryption key, and each data record generates its own independent random initialization vector. This ensures that the same plaintext encoded data produces different attribute ciphertext data in different data records. The attribute ciphertext data is then associated with and stored with the index labels of the corresponding second-level leaf nodes, forming a mapping relationship between index labels and attribute ciphertext data. Finally, an encrypted dataset carrying an attribute label tree index is generated.

[0030] After the encrypted dataset carrying the attribute label tree index is generated, the attribute reduction process begins. The core objective of attribute reduction is to remove redundant attributes from the conditional attribute set that do not contribute to the data's distinguishing ability, retaining the smallest subset of attributes while maintaining the original distinguishing ability. The entire reduction process is completed in the ciphertext field, without the need to decrypt the attribute ciphertext data. Its feasibility stems from the fact that the index labels themselves carry equivalence information about the attribute values—two encrypted data records have the same index label for a certain attribute if and only if their encoded values ​​for that attribute fall within the same range of index values.

[0031] First, a query token is constructed to locate the target attribute without decrypting the attribute ciphertext data. The query token construction process is symmetrical to the index tag generation process. Using the node master key as the key, and the path code, number value range, and current synchronization cycle identifier of the target attribute as input, a pseudo-random function is invoked to generate the query token. Since the inputs of the query token and the corresponding index tag are completely identical, and the same pseudo-random function and the same node master key are used, the query token and the index tag of the target attribute are numerically perfectly matched. By comparing the matching relationship between the query token and the index tag, the second-level leaf node corresponding to the target attribute can be located without accessing the underlying attribute ciphertext data.

[0032] Based on the index labels, the value range information associated with each level 2 leaf node is extracted. A conditional attribute set is constructed using the attribute identifiers corresponding to all level 2 leaf nodes in the attribute label tree index structure. This conditional attribute set is the complete set of all attributes participating in the reduction analysis. In the aforementioned specific implementation scenario, the conditional attribute set includes seven attribute identifiers: temperature, vibration, pressure, fault description, operation record, operating status, and load status.

[0033] Construct indistinguishable relations on a set of conditional attributes. Indistinguishable relations are a core concept in rough set theory, used to describe equivalence relations between objects that are indistinguishable under a given set of attributes. For any two encrypted data records in an encrypted dataset with attribute label tree indexes, iterate through each attribute in the conditional attribute set, comparing the index labels of the two encrypted data records on the corresponding attributes to determine indistinguishability. If all index labels of the two encrypted data records are the same on a subset of attributes in the conditional attribute set, then the two encrypted data records are determined to be indistinguishable with respect to that subset of attributes. For example: Assume the encrypted dataset contains 200 encrypted data records, numbered 1 to 200. Record 1 has an index label value of [value missing] on the temperature attribute. The index label value of record 2 on the temperature attribute is ,like If the index labels of Record 1 and Record 2 are identical across all 7 attributes, then Record 1 and Record 2 are indistinguishable across the entire set of conditional attributes.

[0034] Based on indistinguishable relations, the encrypted dataset carrying an attribute-labeled tree index is divided into several equivalence classes. Within each equivalence class, the index labels of the encrypted data records on all attributes of the conditional attribute set are completely identical, and there is at least one attribute with a different index label between different equivalence classes. Assuming that the index label combinations of 200 encrypted data records across all 7 attributes generate 45 different equivalence classes, then the encrypted dataset is divided into 45 equivalence classes.

[0035] After equivalence class partitioning, a conditional attribute discrimination matrix is ​​constructed. A square matrix with the number of rows and columns equal to the number of equivalence classes is created; in the example above, this is a 45x45 matrix. For any two distinct equivalence classes, each attribute in the conditional attribute set is traversed. If the index labels of the representative records for the corresponding attributes differ between the two equivalence classes, the corresponding attribute identifiers are filled into the cells corresponding to the two equivalence classes in the conditional attribute discrimination matrix. Each cell in the conditional attribute discrimination matrix records the set of all attribute identifiers that can distinguish between two corresponding equivalence classes. For example, if equivalence class 1 and equivalence class 2 differ only in the index labels for the temperature and vibration attributes, then the cell in the first row and second column of the conditional attribute discrimination matrix contains the identifiers for both temperature and vibration. The diagonal cells are empty because they correspond to the same equivalence class. A sparse matrix format is used to store the conditional attribute discrimination matrix, recording only the row and column indices of non-empty cells and the set of attribute identifiers contained in the non-empty cells, thus avoiding storing a large number of empty cells and reducing memory overhead. In the case of 45 equivalence classes, the conditional attribute discrimination matrix has a total of... Each of the upper triangular off-diagonal cells needs to be checked, and only the non-empty parts are actually stored.

[0036] Attribute reduction is performed based on the conditional attribute discrimination matrix. First, the frequency of each attribute identifier in all non-empty cells is counted. A higher frequency indicates a greater role the attribute plays in distinguishing different equivalence classes. Attribute identifiers with a frequency of zero are removed from the conditional attribute set to obtain the candidate attribute set. A frequency of zero indicates that the attribute cannot distinguish between any two equivalence classes; retaining or removing this attribute does not affect the data's discriminative power, therefore it can be directly eliminated.

[0037] The reduced attribute set is initialized as an empty set, and then a greedy strategy is used for iterative selection. Iteratively, the attribute identifier with the highest frequency of occurrence in uncovered non-empty cells is selected from the candidate attribute set and added to the reduced attribute set. The strategy of selecting the highest frequency is based on the idea of ​​greedy optimization; at each step, the attribute with the strongest current coverage capability is selected, thus covering all non-empty cells with as few attributes as possible. Non-empty cells containing the corresponding attribute identifier are marked as covered, indicating that the equivalence class pairs corresponding to these non-empty cells can be distinguished by the attributes in the reduced attribute set. This iteration is repeated until all non-empty cells are covered, at which point the reduced attribute set is the smallest subset of attributes that maintains complete distinguishing ability. For example, suppose the initial frequencies of the 7 attributes in 990 non-empty cells are: temperature 820 times, vibration 785 times, pressure 340 times, fault description 760 times, operation record 120 times, running status 680 times, and load status 95 times. In the first iteration, the temperature attribute, which appears most frequently, is added to the reduced attribute set. The 820 non-empty cells containing the temperature attribute identifier are marked as covered, leaving 170 uncovered cells. In the second iteration, the frequency of the remaining attributes in the 170 uncovered cells is recalculated. Assuming the fault description has the highest frequency of 145 occurrences in the uncovered cells, it is added to the reduced attribute set. This process is repeated until all non-empty cells are covered. The final reduced attribute set may contain three attributes: temperature, fault description, and operating status. The original seven attributes are reduced to three, significantly reducing the data dimensionality for subsequent fusion processing while maintaining complete distinguishability.

[0038] In one alternative implementation, when multiple attribute identifiers appear with the same frequency in uncovered cells, the following strategy can be used for selection: prioritize the attribute with a shallower level in the attribute label tree index structure, i.e., the attribute with a smaller level 1 child node number; if it is still impossible to distinguish, select according to the lexicographical order of the attribute identifiers.

[0039] Attribute projection is performed on the encrypted dataset carrying the attribute label tree index based on the reduced attribute set. The attribute projection operation retains the attribute ciphertext data and index labels corresponding to the attribute identifiers in the reduced attribute set, while removing the attribute ciphertext data and index labels corresponding to other attribute identifiers. In the example above, the attribute ciphertext data and index labels for the three attributes of temperature, fault description, and operating status are retained, while the attribute ciphertext data and index labels for the four attributes of vibration, pressure, operation record, and load status are removed. After attribute projection, a reduced encrypted dataset is generated. Each encrypted data record in the reduced encrypted dataset contains only the attribute ciphertext data and index labels of each attribute in the reduced attribute set, reducing the data dimension from seven attributes to three. The reduced encrypted dataset will serve as the input for the hierarchical nested Copula fusion processing in step 3.

[0040] It should be noted that the entire attribute reduction process, from constructing indistinguishable relations, partitioning equivalence classes, constructing conditional attribute discrimination matrices, to greedy iterative selection, is completed on the ciphertext domain through the comparison of index labels, without involving the decryption of attribute ciphertext data. This characteristic ensures that the original data of each edge computing node remains encrypted during the attribute reduction stage, and even the computing entity performing the reduction operation cannot obtain the plaintext data content, thus achieving simultaneous privacy protection and data dimensionality reduction.

[0041] First, the reduced encrypted dataset is grouped according to the edge computing node affiliation. Each encrypted data record in the reduced encrypted dataset carries the identification information of its source edge computing node. Based on this identification information, the reduced encrypted dataset is split into multiple edge node reduced encrypted data subsets, each containing only encrypted data records from the same edge computing node. In an industrial monitoring scenario with 5 edge computing nodes, the reduced encrypted dataset will be split into 5 edge node reduced encrypted data subsets. The significance of this grouping operation is that data collected by different edge computing nodes often differ in physical characteristics and statistical distribution. Grouping ensures that subsequent edge distribution transformation and dependency modeling are performed independently within each node, thereby accurately capturing the data distribution characteristics of each node and avoiding modeling distortion caused by mixing the distribution characteristics of different nodes.

[0042] After grouping, a global object identifier is assigned to each data record. The global object identifier consists of a data acquisition time window index and a business object code. The data acquisition time window index identifies the acquisition period to which the data record belongs. For example, in a system with a 10-minute acquisition cycle, the first acquisition cycle corresponds to a time window index of 1, the second acquisition cycle to a time window index of 2, and so on. The business object code identifies the specific physical entity or logical object being observed, such as device number P0037 on a production line. Combining the data acquisition time window index and the business object code uniquely identifies data records belonging to the same observation object within the same time window on different edge computing nodes. This identification mechanism provides a foundation for record alignment in subsequent cross-node data fusion, because only multidimensional data belonging to the same observation object within the same time period has significance for joint analysis. In an optional implementation, the global object identifier is generated using string concatenation, for example, concatenating the time window index "TW0042" with the business object code "P0037" to form "TW0042-P0037" as the global object identifier.

[0043] Next, the reduced encrypted data subsets at each edge node are decrypted. For each edge computing node, the attribute ciphertext data in the reduced encrypted data subset is decrypted using the corresponding node master key to obtain the reduced plaintext data subset. The decryption process is the reverse operation of the data encryption sub-process in step 1. That is, the attribute encryption key is recovered by calling the key derivation function using the node master key and the path encoding of each second-level leaf node, and then a symmetric decryption operation is performed on the attribute ciphertext data using the stored random initialization vector to restore the encoded plaintext data of each attribute. The decryption operation is performed locally on each edge computing node or on the trusted aggregation node to ensure that the attribute ciphertext data can only be restored in an environment with the correct node master key, thereby maintaining the privacy protection characteristics of the data throughout the entire fusion processing chain.

[0044] After obtaining the simplified plaintext data subset of the edge nodes, edge distribution transformation is performed. The purpose of edge distribution transformation is to convert the original values ​​of each attribute into a unified probability scale, enabling dependency analysis of attributes with different dimensions and value ranges within the same probability space. This transformation is based on the fundamental principle of probability integral transformation, namely, that for any continuous random variable, its empirical distribution function value follows a uniform distribution. The specific execution process is as follows: For each attribute in the simplified attribute set, all values ​​of the corresponding attribute in the simplified plaintext data subset of the edge nodes are extracted to form an attribute value sequence. Assuming that an attribute has 200 value records on a certain edge computing node, the length of the corresponding attribute value sequence is 200. The attribute value sequence is sorted in ascending order, and a rank is assigned to each attribute value, starting from 1 and increasing. When there are duplicate values, the average rank method is used. The rank of each attribute value is divided by the length of the attribute value sequence and then incremented by 1 to obtain the edge probability integral transformation value. The design of using the attribute value sequence length plus 1 in the denominator, rather than the attribute value sequence length itself, ensures that all marginal probability integral transformation values ​​strictly fall within the open interval of 0 to 1, avoiding extreme values ​​of 0 or 1, as the Copula function may become numerically unstable at boundary points. For example, with an attribute value sequence length of 200, the marginal probability integral transformation value corresponding to the attribute value with rank 1 is... ,in This represents the marginal probability integral transform value, where the numerator is the rank of the corresponding attribute value, and the denominator is the length of the attribute value sequence plus 1. The marginal probability integral transform value corresponding to the attribute value with a rank of 200 is... The above transformation converts all values ​​of the corresponding attribute into a sequence of marginal probability integral transformation values ​​located in the open interval between 0 and 1. In an optional implementation, for discrete attribute values, a small random perturbation is added before assigning ranks to break the parallel relationship, with the perturbation amplitude controlled at one-thousandth of the original value interval.

[0045] After completing the edge distribution transformation, the Kendall rank correlation coefficient is calculated for the attribute pairs within each edge computing node. Compared to the Pearson linear correlation coefficient, the Kendall rank correlation coefficient has the advantage of being independent of the variable distribution shape and can characterize nonlinear monotonic dependencies, which is particularly important for the common nonlinear association patterns in multi-source heterogeneous data. The calculation process of the Kendall rank correlation coefficient is as follows: for any two attributes, the edge probability integral transformation value sequences are paired to form a data pair set. Assume the length of the edge probability integral transformation value sequence is... ,in If the total number of data records in the attribute value sequence is represented, then the data pair set contains... There are 3 data pairs, each consisting of the marginal probability integral transform values ​​of two attributes at the same record location. For any two data pairs in the set, if the difference between the two component values ​​of the first data pair and the two component values ​​of the second data pair has the same sign, they are considered a consistent pair; otherwise, they are considered a non-consistent pair. Specifically, let the first data pair be... The second data pair is ,in and These represent the first attribute in the first position. Article and Section Marginal probability integral transform values ​​on each record and These represent the second attribute in the first position. Article and Section The marginal probability integral transform value on the record, if and If the signs of the two data points are the same (both positive or both negative), then these two data pairs constitute a consistent pair; otherwise, they constitute a inconsistent pair. Consistency means that the changes in the two attributes are correlated; when one attribute increases, the other tends to increase as well. The Kendall rank correlation coefficient is obtained by dividing the difference between the number of consistent pairs and the number of inconsistent pairs by the total number of pairwise combinations. The formula is: ,in This represents the Kendall rank correlation coefficient. This represents the total number of consistent pairs in the data pair set. This represents the total number of non-consistent pairs. Indicates from The total number of combinations of taking 2 items from a data pair, i.e. The range of values ​​for the Kendall rank correlation coefficient is... A value of 1 indicates a perfect positive correlation, a value of -1 indicates a perfect negative correlation, and a value of 0 indicates no monotonic correlation. An intra-node Kendall rank correlation matrix is ​​constructed based on the Kendall rank correlation coefficients of all attribute pairs. The rows and columns of the matrix correspond to the attributes in the reduced attribute set, with all diagonal elements being 1 and the off-diagonal elements representing the Kendall rank correlation coefficients of the corresponding attribute pairs. When the reduced attribute set contains 6 attributes, the intra-node Kendall rank correlation matrix is ​​a 6x6 symmetric square matrix. In an optional implementation, when the number of data records is large, a block sampling method is used to accelerate the calculation of the Kendall rank correlation coefficients. The data pair set is randomly divided into several sub-blocks, and the number of consistent and inconsistent pairs within each sub-block is calculated and then summarized.

[0046] The intra-node Copula dependency parameters are determined based on the intra-node Kendall rank correlation matrix. This step utilizes an important analytical property of Gumbel family Copulas: a deterministic inversion relationship exists between the Kendall rank correlation coefficient and the Gumbel family dependency parameters. The process for determining the Gumbel family dependency parameters is as follows: the Kendall rank correlation coefficient value is converted into a Gumbel family dependency parameter using the parameter inversion relationship of the Gumbel family Copulas. The Gumbel family dependency parameter is equal to the difference between 1 divided by 1 and the absolute value of the Kendall rank correlation coefficient value. The corresponding inversion formula is... ,in Indicates the Gumbel family dependency parameters. This represents the absolute value of the Kendall rank correlation coefficient. The reason for using absolute values ​​is that the Gumbel family Copula itself only characterizes positive correlation dependency structures; negative correlation requires additional processing. When the Kendall rank correlation coefficient is negative, a negative correlation marker is added to the transformed Gumbel family dependency parameters. The negative correlation marker is handled by taking the complement of the marginal probability integral transformation value of one attribute in the negatively correlated attribute pair (i.e., subtracting the original value from 1) during the actual calculation of the joint distribution function, thus transforming the negative correlation into a positive correlation before substituting it into the Gumbel family Copula function. For example, for an attribute pair with a Kendall rank correlation coefficient of 0.6, the corresponding Gumbel family dependency parameters are... For example, for an attribute pair with a Kendall rank correlation coefficient of -0.4, the corresponding Gumbel family dependency parameter is... And attach a negative correlation marker. The range of values ​​for the Gumbel family dependency parameter is... A parameter value of 1 indicates complete independence, while a larger parameter value indicates a stronger dependency. The core reason for choosing the Gumbel family of Copulas as a dependency modeling tool is its nesting closure property, meaning that multiple Gumbel family Copulas can be nested and combined while still maintaining a valid Copula structure. This property is the mathematical basis for constructing subsequent hierarchical nested structures.

[0047] refer to Figure 1 , Figure 1 The horizontal axis represents the marginal probability integral transformation value of attribute 1, and the vertical axis represents the marginal probability integral transformation value of attribute 2. Both axes range from 0 to 1 (open intervals). The graph contains multiple data points, each representing a pair of transformation values ​​obtained after marginal distribution transformation of a data record on attributes 1 and 2. The data points in the data pair set generally show a clustering trend from the lower left to the upper right, reflecting a positive monotonic correlation between attributes 1 and 2. The graph marks the lines connecting several typical data pairs to illustrate the rules for determining consistent and inconsistent pairs. The condition for a consistent pair is: take any two data pairs from the data pair set, let the first data pair be... The second data pair is ,in and Attribute 1 is in the first place. Article and Section Marginal probability integral transform values ​​on each record and Attribute 2 is in the th Article and Section The marginal probability integral transform values ​​on the record, if the difference and difference If the signs of the two attributes are the same, meaning their changes occur in the same direction, they are considered a matching pair. In the diagram, the two data points corresponding to a matching pair are connected by a solid line segment. It can be observed that the data points at both ends of the line show changes in the same direction on both the horizontal and vertical axes; that is, one data point's value on both the horizontal and vertical axes is either greater than or less than the other data point. Conversely, if the difference... and difference If the signs of the two data points are opposite—that is, one attribute increases while the other decreases—they are considered non-consistent pairs. In the diagram, the two data points corresponding to non-consistent pairs are connected by dashed lines. It can be observed that the trends of change of the data points at both ends of the line are opposite in the horizontal direction to those in the vertical direction. Figure 1 The formula for calculating Kendall's rank correlation coefficient is marked in the lower right corner. ,in This represents the Kendall rank correlation coefficient. This represents the total number of identical pairs among all pairwise combinations in the data set. This represents the total number of non-consistent pairs. This represents the total number of data pairs in the data pair set. Indicates from The number of combinations of selecting 2 items from a data pair is... When the data points exhibit a generally positive monotonic trend, the number of consistent pairs far exceeds the number of inconsistent pairs, and the Kendall rank correlation coefficient approaches 1; when the data points are randomly distributed with no obvious trend, the number of consistent and inconsistent pairs is roughly equal, and the Kendall rank correlation coefficient approaches 0. Figure 1 The physical meaning of Kendall's rank correlation coefficient can be intuitively understood; that is, it quantifies the monotonic dependence between two attributes by statistically analyzing the consistency of the direction of change between each pair of data.

[0048] After obtaining the Gumbel family dependency parameters for each attribute pair, a nested Copula structure within a node is constructed. The construction process for this nested Copula structure is as follows: Attributes in the reduced attribute set are hierarchically clustered according to the magnitude of their Gumbel family dependency parameters. The hierarchical clustering strategy follows a strong-to-weak principle, prioritizing the aggregation of attribute pairs with larger Gumbel family dependency parameters to form the lower-level subgroups. The reason for prioritizing the aggregation of the strongest dependency pairs is that the nested structure of the Gumbel family Copula requires that the outer Gumbel family dependency parameter is no greater than the inner Gumbel family dependency parameter. ,in This indicates the dependency parameters of the outer Gumbel family. The Gumbel family dependency parameter represents the inner layer. This constraint ensures the mathematical validity of the nested multivariate joint distribution function. Violating this constraint will cause the joint distribution function to fail to meet the monotonicity requirement of Copula, resulting in meaningless probability values. Each bottom-level subgroup is then aggregated according to the average Gumbel family dependency parameter between subgroups to form a top-level group. This aggregation continues layer by layer until all attributes are grouped into the same top-level group, forming a tree-like nested structure. Taking a reduced attribute set containing 6 attributes as an example, let's assume the 6 attributes are denoted as attributes A1 to A6. If the Gumbel family dependency parameter between attributes A1 and A2 is 3.2, and the Gumbel family dependency parameter between attributes A3 and A4 is 2.8, then in the bottom-level clustering, attributes A1 and A2 are first aggregated into a bottom-level subgroup G1, and attributes A3 and A4 are aggregated into a bottom-level subgroup G2. If attributes A5 and A6 have relatively small Gumbel family dependency parameters with other attributes, for example, average values ​​of 1.5 and 1.3 respectively, then attribute A5 is either assigned to the bottom subgroup G1 or kept separately. In the intermediate layer, the bottom subgroups G1 and G2, along with attributes A5 and A6, are further aggregated according to the average Gumbel family dependency parameters between subgroups to form upper-level groups. Finally, all attributes are included in the top-level group. In an optional implementation, when the number of attributes in the reduced attribute set exceeds 10, the Ward minimum variance criterion is used instead of the simple averaging method to calculate the Gumbel family dependency parameters between subgroups.

[0049] After constructing the nested Copula structure within each node, the next step is to build a cross-node Copula dependency structure. Data collected by different edge computing nodes are often not completely independent. For example, in smart grid scenarios, load data from adjacent substations exhibit spatial correlation, while in industrial IoT scenarios, monitoring data from upstream and downstream processes show causal relationships. Capturing these cross-node dependencies is crucial for global data fusion. The construction process for the cross-node Copula dependency structure is as follows: For any two edge computing nodes, calculate the Frobenius distance between their intra-node Kendall rank correlation matrices. The Frobenius distance is a matrix norm that measures the overall difference between two matrices of the same dimension at the element level. It is calculated by summing the squares of the differences between corresponding elements of the two matrices and taking the arithmetic square root. The formula is: ,in Represents the Frobenius distance. The dimension of the Kendall rank correlation matrix within a node represents the number of attributes in the reduced attribute set. and These represent the in-node Kendall rank correlation matrices of the two edge computing nodes, respectively. Line number The element values ​​of the column. The similarity coefficient between nodes is obtained by subtracting the Frobenius distance from 1 and dividing by the square root of the matrix dimension, using the formula: ,in This represents the similarity coefficient between nodes. Divide by The aim is to normalize the Frobenius distance to a scale independent of matrix dimensions, making the inter-node similarity coefficients calculated under reduced attribute sets of different sizes comparable. When the data distribution characteristics of two edge computing nodes are completely identical, their intra-node Kendall rank correlation matrices are completely identical, the Frobenius distance is 0, and the inter-node similarity coefficient is 1; when the differences are extremely large, the inter-node similarity coefficient approaches 0. In an optional implementation, when the calculated inter-node similarity coefficient is negative, it is truncated to 0.01 to ensure the effectiveness of subsequent Gumbel family parameter inversion. The inter-node similarity coefficient is converted into cross-node Gumbel family dependency parameters through the Gumbel family parameter inversion relationship, also using... Perform the conversion, where This represents the cross-node Gumbel family dependency parameters. A cross-node dependency parameter matrix is ​​constructed based on the cross-node Gumbel family dependency parameters of all edge compute node pairs. The rows and columns of the cross-node dependency parameter matrix correspond to each edge compute node, and the matrix elements are the cross-node Gumbel family dependency parameters of the corresponding node pair. In a scenario with 5 edge compute nodes, the cross-node dependency parameter matrix is ​​a 5x5 symmetric square matrix.

[0050] A hierarchical nested Copula fusion model is constructed based on a node-within-a-node Copula structure and a cross-node dependency parameter matrix. The bottom layer of the hierarchical nested Copula fusion model consists of node-within-a-node Copula structures for each edge computing node, while the top layer is a cross-node nested Copula structure built based on the cross-node dependency parameter matrix. The construction method for the cross-node nested Copula structure is the same as that for the node-within-a-node Copula structure, both employing a hierarchical clustering strategy. Node pairs with larger cross-node Gumbel family dependency parameters are preferentially aggregated to form the bottom-level node group, and then aggregated layer by layer upwards until all edge computing nodes are grouped into the same top layer. This two-layer architecture design allows the fusion model to simultaneously characterize the fine-grained dependencies between attributes within a node and the coarse-grained spatial dependencies between nodes, forming a complete dependency description from local to global.

[0051] refer to Figure 2 The horizontal axis of both subplots represents the marginal probability integral transform value of the first variable. The vertical axis represents the marginal probability integral transform value of the second variable. The values ​​range from 0 to 1. The values ​​marked on the contour lines are the joint distribution function values ​​of the Gumbel family Copula. A higher value indicates a higher joint cumulative probability for the corresponding region. The left subgraph corresponds to the Gumbel family dependency parameters. In the case of weak dependency, the corresponding Kendall rank correlation coefficient is In this subplot, the contour lines exhibit a relatively evenly distributed arc-shaped distribution, transitioning smoothly from the low-value region in the lower left corner to the high-value region in the upper right corner, with relatively uniform spacing between adjacent contour lines. This distribution pattern indicates that when the dependence between two variables is weak, the isoprobability surface of the joint distribution function approximates the product of two independent uniform distributions, and the joint probability value increases at a relatively even rate across the entire unit plane, without any obvious probability concentration regions. The right subplot corresponds to the Gumbel family dependency parameters. In the case of moderate dependence, the Kendall rank correlation coefficient is... Compared to the left subplot, the contour lines in the right subplot begin to converge towards the main diagonal of the unit plane. The contour lines become noticeably denser near the upper right corner, while the spacing widens in the corners further away from the diagonal. This trend of contour lines converging towards the diagonal reflects the joint probability quality beginning to shift towards... and Regions exhibiting both large and small values ​​tend to cluster, meaning that when one variable takes a large value, the other variable also tends to take a large value, reflecting a moderate degree of positive dependency. A comparison of the two subplots shows that as the Gumbel family dependency parameter increases from 1.2 to 2.0, the contour lines gradually converge diagonally from a nearly uniform distribution, indicating the emergence of a probability concentration effect in the joint distribution. The dashed main diagonal serves as a reference line, visually demonstrating the degree of deviation of the contour lines from the direction of perfect positive correlation.

[0052] Data fusion is performed using a hierarchical nested Copula fusion model. The process involves aligning data records across edge computing nodes according to their global object identifiers, grouping records with the same identifier into the same fusion group. This alignment ensures strict matching of the input data for the fusion computation across time and object dimensions. If an edge computing node is missing a data record for a particular observation within a given time window, it is marked as missing in the corresponding fusion group and filled with the marginal probability integral transform value corresponding to the median of the node's marginal distribution; the filler value is 0.5.

[0053] A two-stage joint distribution computation is performed for each fusion group. The first stage is the intra-node joint distribution computation. First, within each edge computation node, the Gumbel family Copula joint distribution function values ​​are calculated layer by layer from the bottom subgroup to the top group according to the nested Copula structure within the node. The general form of the joint distribution function of the Gumbel family Copula is: ,in This represents the joint distribution function value of the Gumbel family of Copulas. Indicates the number of variables participating in the joint calculation. Indicates the first Marginal probability integral transform values ​​of each variable Represents the natural logarithm function. This indicates the Gumbel family dependency parameters for the corresponding layer. This represents the natural exponential function. During the calculation of each layer, the joint distribution function value output from the next layer is used as input and combined with the Gumbel family dependency parameter of the corresponding layer to calculate the joint distribution function value of that layer. Taking the aforementioned six attributes as an example, in the bottom subgroup G1, the marginal probability integral transform values ​​of attributes A1 and A2 are substituted into the Gumbel family Copula joint distribution function, and the calculation is performed using the Gumbel family dependency parameter 3.2 corresponding to the bottom subgroup G1 to obtain the joint distribution function value of the bottom subgroup G1. Similarly, the joint distribution function value of the bottom subgroup G2 is obtained. In the upper-level group, , The marginal probability integral transform values ​​of attributes A5 and A6 are used as inputs, and the calculation is performed using the Gumbel family dependency parameters corresponding to the upper-level group to finally obtain the intra-node joint distribution value of each edge computing node. The intra-node joint distribution value is a scalar value in the interval between 0 and 1, which comprehensively reflects the joint probability level of all reduced attributes on the corresponding edge computing node in the current fusion group. In an optional implementation, for attribute pairs with additional negative correlation labels, before substituting into the Gumbel family Copula joint distribution function, the marginal probability integral transform value of the corresponding attribute is replaced with its complement value, i.e. ,in This represents the integral transform value of the marginal probability after replacement. This represents the original marginal probability integral transform value. After the calculation is completed, the joint distribution function value is corrected accordingly.

[0054] refer to Figure 3 , and Figure 2 A comparison is made to illustrate the changing trends of the joint distribution under conditions of relatively strong dependence and strong dependence. The coordinate settings of the two subplots are... Figure 2 Consistent, with the horizontal axis as The vertical axis is The values ​​range from 0 to 1, and the labeled values ​​on the contour lines represent the joint distribution function values. The left subplot corresponds to the Gumbel family dependency parameters. In cases of strong dependence, the Kendall rank correlation coefficient is In this subplot, the contour lines have clearly compressed and converged towards the main diagonal, especially in the upper right region, where the contour lines are almost parallel to the diagonal and extremely closely spaced, indicating that the joint probability mass is highly concentrated in [the area shown in the image]. and Within a band of similar values, in regions far from the diagonal, such as the upper left and lower right corners, the contour lines are sparse and the values ​​are very low, indicating a very low probability that one variable will have a maximum while the other has a minimum. The physical meaning of this distribution pattern is that under a strong dependency, the values ​​of the two variables exhibit a high degree of coordinated change, making severe inverse deviations almost impossible. The right subplot corresponds to the Gumbel family dependency parameters. In the case of strong dependency, the Kendall rank correlation coefficient is In this subplot, the contour lines further narrow into a narrow band tightly adhering to the main diagonal, with almost all joint probability masses concentrated in a very narrow area near the diagonal. The distribution of the contour lines shows that low-value contour lines occupy the vast majority of the area in the unit plane, while higher-value contour lines appear only in a small region adjacent to the upper right diagonal, forming a steep probability gradient. Figure 2 and Figure 3 A comprehensive comparison of the four subgraphs clearly shows that the Gumbel family depends on parameters. As the value gradually increases from 1.2 to 6.0, the contour lines gradually compress from an approximately uniform arc-shaped distribution to a band-like distribution closely following the diagonal, indicating a continuous increase in the concentration of joint probability mass. This characteristic of Gumbel family Copulas allows them to be expressed through a single parameter. The Gumbel family of Copulas offers flexible control over the strength of dependencies between variables, ranging from near independence to strong positive correlation, providing an adjustable parameterization tool for differentiated modeling of dependencies between different levels in hierarchical nested Copula fusion models. Furthermore, Copulas exhibit strong ability to capture joint extreme events in the upper tail region; when two variables simultaneously reach their maxima, the decay rate of the joint probability is slower than in the independent case. This asymmetric tail characteristic is helpful in identifying extreme conditions of multi-node collaborative anomalies in multi-source heterogeneous data fusion.

[0055] The second stage is the cross-node joint distribution calculation. Following a cross-node nested Copula structure, the global joint distribution value is calculated using the intra-node joint distribution values ​​of each edge computing node as input, combined with cross-node Gumbel family dependency parameters. The calculation method at the cross-node level is completely consistent with that at the intra-node level; the only difference is that the input variables are replaced by the intra-node joint distribution values ​​of each attribute instead of the edge probability integral transformation values, and the Gumbel family dependency parameters are replaced by cross-node Gumbel family dependency parameters. Taking five edge computing nodes as an example, assuming that in the cross-node nested Copula structure, nodes 1 and 2 are aggregated first, with a corresponding cross-node Gumbel family dependency parameter of 2.1, the cross-node joint value of the intra-node joint distribution values ​​of nodes 1 and 2 is calculated first, and then aggregated layer by layer upwards with the intra-node joint distribution values ​​of other nodes. The final output global joint distribution value is a scalar in the interval between 0 and 1, representing the global joint probability level of all reduced attributes on all edge computing nodes in the current fusion group. The closer the global joint distribution value is to 1, the more the values ​​of each attribute and node in the current fusion group tend to be in the high probability region in the sense of joint probability; the closer the global joint distribution value is to 0, the more the current observation is in the low probability tail region of the joint distribution, which may correspond to abnormal operating conditions or rare events.

[0056] Using the global joint distribution value as the joint probability representation of the fused multi-source heterogeneous data, privacy-preserving fusion processing of multi-source heterogeneous data for edge computing nodes is achieved. In one optional implementation, the global joint distribution value is compared with a preset probability threshold. When the global joint distribution value is lower than the preset probability threshold, an anomaly warning is triggered. The preset probability threshold is determined based on the empirical quantiles of the global joint distribution value under normal operating conditions in historical data; for example, the global joint distribution value corresponding to the 5th percentile is taken as the preset probability threshold. In another optional implementation, a sliding window analysis is performed on the global joint distribution value sequence of multiple consecutive time windows. By detecting the continuous downward trend of the global joint distribution value, progressive failures or degradation processes can be identified.

[0057] The present invention has been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of the invention. The descriptions of the embodiments above are merely for the purpose of helping to understand the method and core ideas of the present invention. It should be noted that those skilled in the art can make various improvements and modifications to the present invention without departing from its principles, and these improvements and modifications also fall within the protection scope of the claims of the present invention.

Claims

1. A method for privacy-preserving fusion processing of multi-source heterogeneous data for edge computing nodes, characterized in that, Includes the following steps: Step 1: Obtain multi-source heterogeneous raw data distributed across multiple edge computing nodes, uniformly encode the multi-source heterogeneous raw data based on a preset discretized dictionary, construct an attribute label tree index structure, generate a node master key for each edge computing node, and perform searchable encryption processing based on the node master key to generate an encrypted dataset carrying the attribute label tree index. Step 2: Taking the encrypted dataset with attribute label tree index as input, construct indistinguishable relations on the set of conditional attributes based on the index labels and divide them into equivalence classes, construct the conditional attribute discrimination matrix, perform attribute reduction operation without decrypting the attribute ciphertext data, and generate a reduced encrypted dataset. Step 3: Group and decrypt the reduced encrypted dataset according to the edge computing node affiliation, perform edge distribution transformation processing, determine the Gumbel family dependency parameters based on Kendall rank correlation coefficient, construct nested Copula structures within nodes and cross-node Copula dependency structures to form a hierarchical nested Copula fusion model, perform data fusion operation through the hierarchical nested Copula fusion model, and output the global joint distribution value as the joint probability representation of the fused multi-source heterogeneous data.

2. The method according to claim 1, characterized in that, The multi-source heterogeneous raw data includes numerical sensor data, text log data, and sequential state data. The pre-defined discretization dictionary includes a binning boundary table for numerical sensor data, a vocabulary mapping table for text log data, and time granularity parameters for sequential state data. The pre-defined discretization dictionary is synchronized across all edge computing nodes. The unified encoding process is as follows: the numerical sensor data is discretized and binned according to the binning boundary table to obtain numerical interval numbers; the text log data is segmented and mapped according to the vocabulary mapping table to obtain vocabulary index numbers; and the sequential state data is sliced ​​according to the time granularity parameters to obtain time period index numbers.

3. The method according to claim 1, characterized in that, The construction process of the attribute tag tree index structure is as follows: a root node is created as the data source identifier node. Under the root node, three level 1 child nodes are created, corresponding to the three data types: numerical sensor data, text log data, and sequence status data. Under each level 1 child node, a corresponding number of level 2 leaf nodes are created according to the number of attributes contained in the corresponding data type. Each level 2 leaf node is associated with the number value range of the corresponding attribute.

4. The method according to claim 1, characterized in that, The searchable encryption process includes two sub-processes: index tag generation and data encryption. The index tag generation sub-process is as follows: for each second-level leaf node in the attribute tag tree index structure, the path code from the root node to the corresponding second-level leaf node is extracted. The path code, the range of the number associated with the second-level leaf node, and the current synchronization cycle identifier are used as inputs. The pseudo-random function is called to generate the index tag using the node master key as the key. The data encryption sub-process is as follows: the node master key and the path encoding of each second-level leaf node are used as input to call the key derivation function to generate the attribute encryption key. A random initial vector is generated for each data record. The attribute encryption key and the random initial vector are used to symmetrically encrypt the encoded data of each attribute in the data record to obtain the attribute ciphertext data. The attribute ciphertext data is associated with and stored with the index label of the corresponding second-level leaf node.

5. The method according to claim 1, characterized in that, In step 2, a query token is constructed to locate the target attribute without decrypting the attribute ciphertext data. The process of constructing the query token is as follows: using the node master key as the key, and the path code, number value range, and current synchronization cycle identifier of the target attribute as input, a pseudo-random function is called to generate the query token. The second-level leaf node corresponding to the target attribute is located by comparing the matching relationship between the query token and the index label. The process of constructing the indistinguishability relationship is as follows: for any two encrypted data records in the encrypted dataset carrying the attribute label tree index, each attribute in the condition attribute set is traversed. The indistinguishability is determined by comparing whether the index labels of the two encrypted data records on the corresponding attribute are the same. If all the index labels of the two encrypted data records on a certain attribute subset of the condition attribute set are the same, then the two encrypted data records are determined to be indistinguishable with respect to the corresponding attribute subset. Based on indistinguishable relations, the encrypted dataset carrying the attribute label tree index is divided into several equivalence classes.

6. The method according to claim 5, characterized in that, The construction process of the conditional attribute discrimination matrix is ​​as follows: create a square matrix with the number of rows and columns equal to the number of equivalence classes. For any two different equivalence classes, traverse each attribute in the conditional attribute set. If the index labels of the representative records of the two equivalence classes on the corresponding attributes are different, fill the corresponding attribute identifier into the cells corresponding to the two equivalence classes in the conditional attribute discrimination matrix. The conditional attribute discrimination matrix is ​​stored in sparse matrix format. The attribute reduction operation is performed as follows: The frequency of each attribute identifier in all non-empty cells is counted. Attribute identifiers with a frequency of zero are removed from the conditional attribute set to obtain a candidate attribute set. The reduced attribute set is initialized to an empty set. Iteratively, the attribute identifier with the highest frequency in uncovered non-empty cells is selected from the candidate attribute set and added to the reduced attribute set. Non-empty cells containing the corresponding attribute identifier are marked as covered. This iteration is repeated until all non-empty cells are covered. Attribute projection is performed on the encrypted dataset carrying the attribute label tree index based on the reduced attribute set. The attribute ciphertext data and index labels corresponding to the attribute identifiers in the reduced attribute set are retained, while the attribute ciphertext data and index labels corresponding to other attribute identifiers are removed, generating a reduced encrypted dataset.

7. The method according to claim 1, characterized in that, In step 3, the reduced encryption dataset is grouped according to the edge computing node affiliation to obtain multiple edge node reduced encryption data subsets. A global object identifier is assigned to each data record. The global object identifier consists of the data acquisition time window index and the business object code. For each edge computing node, the attribute ciphertext data in the edge node reduced encryption data subset is decrypted using the corresponding node master key to obtain the edge node reduced plaintext data subset. The execution process of edge distribution transformation is as follows: For each attribute in the reduced attribute set, extract all values ​​of the corresponding attribute in the reduced plaintext data subset of the edge node to form an attribute value sequence. Sort the attribute value sequence in ascending order and assign a rank to each attribute value. Divide the rank of each attribute value by the length of the attribute value sequence and add 1 to obtain the edge probability integral transformation value. Convert all values ​​of the corresponding attribute into an edge probability integral transformation value sequence located in the open interval between 0 and 1.

8. The method according to claim 7, characterized in that, The calculation process of Kendall's rank correlation coefficient is as follows: For any two attributes, the marginal probability integral transformation value sequence is paired to form a data pair set. For any two data pairs in the data pair set, if the difference between the two component values ​​of the first data pair and the two component values ​​of the second data pair has the same sign, they are determined to be a consistent pair; otherwise, they are determined to be a non-consistent pair. The difference between the number of consistent pairs and the number of non-consistent pairs is divided by the total number of pairwise combinations to obtain the Kendall's rank correlation coefficient. Based on the Kendall's rank correlation coefficients of all attribute pairs, the intra-node Kendall's rank correlation matrix is ​​constructed. The process of determining the Gumbel family dependency parameters is as follows: The Kendall's rank correlation coefficient value is converted into a Gumbel family dependency parameter using the parameter inversion relation of the Gumbel family Copula. The Gumbel family dependency parameter is equal to 1 divided by 1 minus the absolute value of the Kendall's rank correlation coefficient value. When the Kendall's rank correlation coefficient value is negative, a negative correlation label is added to the converted Gumbel family dependency parameter.

9. The method according to claim 8, characterized in that, The process of constructing a nested Copula structure within a node is as follows: Attributes in the reduced attribute set are hierarchically clustered according to the magnitude of the Gumbel family dependency parameters between attribute pairs. Attribute pairs with larger Gumbel family dependency parameters are preferentially aggregated to form bottom-level subgroups. Each bottom-level subgroup is then aggregated according to the average Gumbel family dependency parameter between subgroups to form upper-level groups. This aggregation is repeated layer by layer until all attributes are grouped into the same top-level group to form a tree-like nested structure. The process of constructing a cross-node Copula dependency structure is as follows: For any two edge computing nodes, the Frobenius distance between the intra-node Kendall rank correlation matrices of the two edge computing nodes is calculated. The quotient obtained by subtracting the Frobenius distance from 1 and dividing it by the square root of the matrix dimension is used as the node similarity coefficient. The node similarity coefficient is converted into cross-node Gumbel family dependency parameters through the Gumbel family parameter inversion relationship. A cross-node dependency parameter matrix is ​​constructed based on the cross-node Gumbel family dependency parameters of all edge computing node pairs.

10. The method according to claim 9, characterized in that, The bottom layer of the hierarchical nested Copula fusion model consists of nested Copula structures within each edge computing node, while the top layer consists of nested Copula structures across nodes constructed based on the cross-node dependency parameter matrix. The data fusion operation is performed as follows: Data records of each edge computing node are aligned according to the global object identifier, and data records with the same global object identifier are grouped into the same fusion group. For each fusion group, the Gumbel family Copula joint distribution function value is first calculated layer by layer from the bottom subgroup to the top group within each edge computing node according to the nested Copula structure. During each layer's calculation, the joint distribution function value output by the lower layer is used as input and combined with the Gumbel family dependency parameters of the corresponding layer to calculate the joint distribution function value of the corresponding layer, thus obtaining the intra-node joint distribution value of each edge computing node. Then, the global joint distribution value is calculated according to the cross-node nested Copula structure, using the intra-node joint distribution value of each edge computing node as input and combining the cross-node Gumbel family dependency parameters.

Images