An industrial equipment state perception method based on a PageRank graph calculation algorithm

Abstract

The application discloses an industrial equipment state perception method based on a PageRank graph calculation algorithm, comprising the following steps: collecting operation data and preprocessing to construct a node set and three types of adjacency matrices; calculating gate weights on the three types of adjacency matrices and generating a fused adjacency matrix through weighted fusion; inputting an initial state into an improved APPNP with the fused adjacency matrix to execute risk-enhanced propagation to generate a first-stage representation; applying a decay factor in the middle of the propagation to generate a second-stage representation and record a path; executing a stay propagation in the late stage of the propagation to generate a third-stage representation and output a path set; respectively propagating and performing weighted fusion with a health score and a key level vector, calculating local and cross-layer differences, and executing residual fusion to generate a state perception vector; and slidingly counting the state perception vector to generate a propagation trace path set. The application realizes accurate perception and abnormal trace of the industrial equipment state, and improves detection accuracy and interpretability.

Description

Technical Field

[0001] This invention relates to the field of industrial equipment condition monitoring technology, and in particular to an industrial equipment condition perception method based on the PageRank graph calculation algorithm. Background Technology

[0002] In the application of Industrial Internet of Things (IIoT), real-time perception and anomaly detection of equipment operating status are crucial for ensuring production continuity and reducing maintenance costs. In existing technologies, common methods rely on single sensor data analysis or anomaly judgment based on statistical thresholds. These methods can identify obvious equipment anomalies to a certain extent, but they are difficult to fully capture the coupling relationship between multiple data sources. As the scale of industrial systems expands, the process dependence, energy transmission, and communication interaction between equipment continue to increase. Single-dimensional data processing methods are prone to overlooking potential anomaly transmission links in complex network structures, resulting in insufficient detection accuracy and limited traceability capabilities.

[0003] In recent years, some studies have applied graph neural networks to industrial equipment state perception tasks, which can improve feature representation capabilities by utilizing the topological information of nodes and edges. However, in the specific implementation process, existing methods generally rely on fixed adjacency structures and fail to perform differentiated modeling for the three types of relationships: process flow, energy flow, and communication links. This results in a failure to reasonably distinguish the contributions of different relationship dimensions to state propagation. Moreover, in the propagation calculation process, common methods often directly adopt a single iterative neighborhood aggregation mechanism, which has the problem of overly smooth propagation, easily weakening the influence of key nodes, and also making it difficult to form an effective response to nodes with sudden state changes.

[0004] In the anomaly detection phase, most existing methods are limited to static threshold judgments and lack modeling of the dynamic changes in device status during multi-stage propagation. Due to the lack of residual compensation mechanisms for local state differentiation and cross-layer differentiation, the sensitivity characteristics of anomaly nodes are often weakened after multiple rounds of propagation, resulting in low accuracy of detection results. Existing technologies are also insufficient in terms of interpretability, making it difficult to provide a causal link for the formation and spread of anomalies through propagation path records, thus limiting the application value of the results in practical operation and maintenance scenarios.

[0005] Therefore, how to provide a method for industrial equipment state perception based on the PageRank graph calculation algorithm is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0006] One objective of this invention is to propose an industrial equipment status perception method based on the PageRank graph calculation algorithm. This invention introduces an improved APPNP propagation structure, integrates process flow, energy flow and communication chain adjacency matrix, and combines health score vector and key level vector to construct a multi-stage propagation and residual fusion mechanism, thereby realizing accurate equipment status modeling and anomaly tracing. It has the advantages of high detection accuracy, strong interpretability and wide applicability.

[0007] An industrial equipment state perception method based on the PageRank graph calculation algorithm according to an embodiment of the present invention includes the following steps:

[0008] Collect operational data from industrial equipment, preprocess and construct a set of industrial equipment nodes and three types of adjacency matrices, calculate health score vectors and key level vectors based on operational data, normalize them to form state prior vectors, and concatenate them with the set of node feature vectors to obtain the initial state input;

[0009] Calculate the gate weights for the three types of adjacency matrices, and perform weighted fusion according to the gate weights to obtain the fused adjacency matrix;

[0010] The improved APPNP propagation structure combines the initial state input with the fused adjacency matrix input to amplify the propagation intensity of abnormally high-risk nodes in the initial propagation stage, generating a stage-one propagation representation.

[0011] During the middle of the propagation, a decay factor is applied to the propagation representation of stage one to obtain the propagation representation of stage two, and the propagation path information of the adjacent edges of each node is recorded.

[0012] In the later stage of propagation, a residual propagation is performed on the propagation representation of stage two to obtain the propagation representation of stage three, and the propagation path record set is output.

[0013] Based on the propagation path record set, structural dependency paths and anomaly sensitive paths are extracted, and propagation operations are performed separately to obtain structural dependency propagation representation sets and anomaly sensitive propagation representation sets. Based on the weighted fusion of health score vector and key level vector, a dual-path fusion state representation set is generated, and local state difference and cross-layer difference are calculated. Residual fusion is performed to obtain the industrial equipment state perception vector set.

[0014] A sliding time window is used to statistically analyze the set of state perception vectors of industrial equipment, and a set of abnormal equipment is output based on the deviation score threshold. The set of propagation path records is then combined to generate a set of propagation tracing paths.

[0015] Optionally, the industrial equipment operating data includes temperature data, vibration data, current data, power data, and communication data. The preprocessing steps include time alignment, noise reduction, and normalization of the operating data. The three types of adjacency matrices include process flow adjacency matrix, energy flow adjacency matrix, and communication link adjacency matrix.

[0016] Optionally, the step of calculating the health score vector and key level vector based on operational data includes:

[0017] The average temperature and temperature fluctuation amplitude are calculated from the temperature data; the root mean square value of vibration and frequency domain energy are calculated from the vibration data; the average current and peak current are calculated from the current data; the active power and power factor are calculated from the power data; and the packet loss rate and delay rate are calculated from the communication data. The calculation results are combined into a health score vector.

[0018] The in-degree and out-degree of each node are calculated in the process flow adjacency matrix, the energy transfer intensity of each node is calculated in the energy flow adjacency matrix, and the connection stability of each node is calculated in the communication link adjacency matrix. The in-degree, out-degree, energy transfer intensity, and connection stability are combined into a key level vector.

[0019] Optionally, the generation process of the stage-one propagation representation in the improved APPNP propagation structure includes: performing row-wise normalization on the fused adjacency matrix to obtain a normalized fused adjacency matrix; setting a quantile threshold q based on the health score vector, selecting nodes with health score values ​​lower than q as high-risk nodes, and generating a risk gating vector composed of 0 and 1 according to the node index; setting a quantile threshold p based on the critical level vector, selecting nodes with critical level values ​​higher than p as critical nodes, and generating a critical gating vector composed of 0 and 1 according to the node index; applying gating to the normalized fused adjacency matrix, retaining the edges where the risk gating vector corresponding to the source node is 1 and the critical gating vector corresponding to the target node is 1, and setting other edges to zero to obtain a stage-one gated adjacency matrix; performing neighborhood aggregation operation on the initial state input and the stage-one gated adjacency matrix, performing row-weighted summation to obtain the first neighborhood aggregation result, and generating the seeding and back-injection result by linear combination of the propagation coefficient α1 and the state prior vector;

[0020] The neighbor comparison gain processing is performed on the seeding and injection results. The difference between each node and the mean of its next-order neighbor in the stage-1 gated adjacency matrix is ​​calculated. The positive difference interval is amplified by the gain coefficient g1, while the non-positive difference interval remains unchanged to obtain the amplified result.

[0021] The amplified result is subjected to interval pruning and normalization. Items exceeding the upper limit are taken from the upper limit, and items below the lower limit are taken from the lower limit. The result is linearly scaled to the range [0,1] within a fixed interval to obtain the stage-1 propagation representation. The propagation path is recorded based on the stage-1 gated adjacency matrix and the first neighborhood aggregation result. The recording rule is to calculate the actual contribution value to the target node for each retained edge and filter out edges with contribution values ​​lower than the threshold τ1 to obtain the stage-1 propagation path record set.

[0022] Optionally, the generation process of the stage two propagation representation in the improved APPNP propagation structure includes:

[0023] The phase-one propagation representation is analyzed sequentially by sliding time window. The mean μ and standard deviation σ of each node within the window are calculated. The difference d between the current value of the node and the mean μ in the phase-one propagation representation is calculated to obtain the amplitude of node state change.

[0024] A nonlinear attenuation factor is constructed based on the magnitude of node state abrupt changes. This nonlinear attenuation factor is determined by the basic attenuation coefficient β, the exponential attenuation function, and the magnitude correction function. When the difference d is greater than zero, the attenuation factor is calculated using the following formula: ;

[0025] When the difference d is less than zero, the formula for calculating the attenuation factor is: ;

[0026] Generate a dynamic decay vector for each node;

[0027] The second neighborhood aggregation operation is performed on the propagation representation of the first stage and the fused adjacency matrix. The propagation values ​​of all neighboring nodes are collected for the target node, and the weighted sum is calculated according to the normalized adjacency edge weights to obtain the second neighborhood aggregation result.

[0028] The second neighborhood aggregation result is multiplied element-wise with the dynamic decay vector to obtain the decay-controlled propagation output;

[0029] A structural balance term is superimposed on the attenuation-controlled propagation output. The structural balance term is generated by multiplying the key level vector with the corresponding value in the fusion adjacency matrix to obtain the compensated propagation result.

[0030] The compensated propagation result is linearly weighted and fused with the state prior vector to output the stage 2 propagation representation.

[0031] In the Phase 2 propagation representation, the weighted contribution value of each edge to the target node during the neighborhood aggregation process is calculated. The edges are sorted according to the weighted contribution value, and only the top k% of the edges are retained as valid paths, forming a set of Phase 2 propagation path records.

[0032] Optionally, the generation process of the stage three propagation representation in the improved APPNP propagation structure includes:

[0033] Element-wise difference is performed between the propagation representation of stage two and the propagation representation of stage one to obtain the cross-stage residual vector;

[0034] For stage two propagation, the difference Δ between the mean μt and the current value vt is calculated using a sliding time window, and a long-term memory factor is constructed using the following formula: ;

[0035] In the fused adjacency matrix, only stable edges that appear in both the propagation path record set of stage one and the propagation path record set of stage two are retained to obtain a stable adjacency matrix.

[0036] The third neighborhood aggregation operation is performed on the second-stage propagation representation and the stable adjacency matrix. The values ​​of the stable neighbor nodes are collected for the target node, and the values ​​are weighted and summed according to the corresponding values ​​in the stable adjacency matrix to obtain the third neighborhood aggregation result.

[0037] The third neighborhood aggregation result is multiplied element-wise with the long-term memory factor, and the cross-stage residual vector is added to obtain the retention compensation propagation output. The retention compensation propagation output is then weighted and fused with the state prior vector to output the stage three propagation representation.

[0038] In the third-stage propagation representation, the propagation path is recorded. The recording rule is to retain only the edges that appear in all three stages of the propagation path record set, thus forming the third-stage propagation path record set.

[0039] Optionally, the process of extracting structural dependency paths and anomaly-sensitive paths based on the propagation path record set, and performing propagation operations respectively, includes:

[0040] In the set of propagation path records in stage three, edges that exist simultaneously in the process flow adjacency matrix, energy flow adjacency matrix, and communication chain adjacency matrix are selected to construct a set of structurally dependent paths;

[0041] In the set of propagation path records in stage three, by combining the state mutation amplitude sequence, the edges associated with nodes whose mutation amplitude is greater than the threshold δ are selected to construct the set of abnormal sensitive paths.

[0042] The neighborhood aggregation operation is performed on the adjacency submatrix corresponding to the propagation representation of the third stage and the set of structural dependency paths. For each target node, the values ​​are collected from the nodes directly connected to the target node in the set of structural dependency paths, and a weighted sum is performed according to the values ​​in the adjacency submatrix to obtain the structural dependency propagation result vector.

[0043] The neighbor aggregation operation is performed on the adjacency submatrix corresponding to the stage 3 propagation representation and the set of abnormal sensitive paths. For each node, the values ​​are collected from the abnormal sensitive neighbor nodes of the node and the values ​​in the adjacency submatrix are weighted and summed to obtain the abnormal sensitive propagation result vector.

[0044] The structure dependency propagation result vector is normalized to generate a set of structure dependency propagation representations;

[0045] The anomaly-sensitive propagation result vector is normalized to generate an anomaly-sensitive propagation representation set.

[0046] Optionally, the process of calculating the local state difference and cross-layer difference and performing residual fusion to obtain the industrial equipment state perception vector set includes:

[0047] In the dual-path fusion state representation set, for each target node, its first-order neighbor nodes in the fusion adjacency matrix are extracted, and the difference between the target node value and the mean of the values ​​of all first-order neighbor nodes is calculated to form a local state difference vector.

[0048] The propagation representations of stage one, stage two, and stage three are compared layer by layer, and the numerical differences of the same node in adjacent propagation stages are calculated to form a cross-layer difference vector.

[0049] The local state difference vector and the cross-layer difference vector are concatenated according to the node index and normalized to obtain the set of state difference feature vectors.

[0050] The set of state difference feature vectors is added element by element to the set of dual-path fusion state representations to form a preliminary residual fusion result;

[0051] A residual amplification function is applied to the preliminary residual fusion result. When the local state difference is positive, it is amplified by the amplification factor g2. When the local state difference is zero or negative, it remains unchanged to obtain the amplified residual fusion result.

[0052] The amplified residual fusion result is normalized and numerically pruned, and the numerical values ​​are mapped to the interval [0,1] and output as a set of industrial equipment state perception vectors.

[0053] Optionally, the process of outputting the abnormal equipment set based on the deviation score threshold includes: performing sliding time window statistics on the industrial equipment state perception vector set, calculating the mean and standard deviation of each node within the window, generating a standardized deviation score vector, marking nodes in the standardized deviation score vector with values ​​greater than a set threshold as abnormal nodes, and outputting the abnormal equipment set composed of the abnormal nodes.

[0054] The beneficial effects of this invention are:

[0055] (1) By calculating the gating weights of the process flow adjacency matrix, energy flow adjacency matrix and communication link adjacency matrix and performing weighted fusion, a fused adjacency matrix is ​​formed. This matrix can comprehensively express multi-dimensional relationship features in a unified structure, avoid the information loss problem caused by a single adjacency structure, and thus enhance the comprehensiveness of equipment state modeling.

[0056] (2) By introducing a multi-stage propagation mechanism through the improved APPNP propagation structure, the first stage enhances the propagation of high-risk nodes, the second stage suppresses the unstable diffusion caused by state mutation through the nonlinear decay factor, and the third stage uses the long-term memory factor and cross-stage residual compensation to maintain the long-term influence of stable nodes, effectively solving the problems of excessive smoothing and weakening of abnormal features.

[0057] (3) By calculating the local state difference and cross-layer difference and performing residual fusion, a set of industrial equipment state perception vectors is generated. Combined with the deviation score threshold, a set of abnormal equipment is output. At the same time, a set of propagation source tracing paths is formed by using propagation path records. This not only improves the accuracy of anomaly detection, but also provides a causal link for anomaly formation and diffusion, enhancing the interpretability and practical operation and maintenance value of the method. Attached Figure Description

[0058] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0059] Figure 1 This is an overall flowchart of an industrial equipment state perception method based on the PageRank graph calculation algorithm proposed in this invention;

[0060] Figure 2 This is a schematic diagram of the improved APPNP multi-stage propagation process of an industrial equipment state perception method based on the PageRank graph calculation algorithm proposed in this invention.

[0061] Figure 3 This is a schematic diagram of the anomaly detection and propagation tracing path output of an industrial equipment state perception method based on the PageRank graph calculation algorithm proposed in this invention. Detailed Implementation

[0062] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, illustrating only the basic structure of the invention, and therefore only show the components relevant to the invention.

[0063] refer to Figure 1-3 A method for industrial equipment state perception based on the PageRank graph calculation algorithm includes the following steps:

[0064] Collect operational data from industrial equipment, preprocess and construct a set of industrial equipment nodes and three types of adjacency matrices, calculate health score vectors and key level vectors based on operational data, normalize them to form state prior vectors, and concatenate them with the set of node feature vectors to obtain the initial state input;

[0065] Gating weights are calculated for the three types of adjacency matrices, and weighted fusion is performed according to the gating weights to obtain a fused adjacency matrix. In a specific embodiment of the present invention, the process of generating the fused adjacency matrix is ​​as follows:

[0066] We construct process flow adjacency matrices, energy flow adjacency matrices, and communication link adjacency matrices respectively. These three types of adjacency matrices reflect the topological relationships of industrial equipment in three dimensions: process flow, energy transmission, and communication connection. The values ​​of the elements in each matrix are used to indicate whether there is a connection between nodes. If there is a connection, the value is non-zero; if there is no connection, the value is zero.

[0067] For each type of adjacency matrix, its gating weight is calculated. The gating weight is calculated based on indicators such as the number of edges connected to the node in the matrix, the stability of the edges, and the importance of this type of relationship to the operation of the equipment. Taking the energy flow adjacency matrix as an example, the energy input and output balance and current fluctuation amplitude of the node are comprehensively considered during the calculation. If the node plays a more significant role in the energy flow, its gating weight is relatively higher. The weight of the process flow adjacency matrix is ​​determined by the criticality of the equipment in the process chain, and the weight of the communication chain adjacency matrix is ​​determined by communication quality indicators such as link delay and packet loss rate.

[0068] The three types of adjacency matrices are multiplied element-wise with their corresponding gating weights to obtain the weighted process flow adjacency matrix, the weighted energy flow adjacency matrix, and the weighted communication link adjacency matrix. Finally, the three weighted matrices are added element-wise according to the node positions to obtain the fused adjacency matrix. The fused adjacency matrix numerically reflects the comprehensive influence of the three types of relationships and can simultaneously take into account the structural characteristics of process dependence, energy transmission, and communication connection.

[0069] The improved APPNP propagation structure combines the initial state input with the fused adjacency matrix input to amplify the propagation intensity of abnormally high-risk nodes in the initial propagation stage, generating a stage-one propagation representation.

[0070] During the middle of the propagation, a decay factor is applied to the propagation representation of stage one to obtain the propagation representation of stage two, and the propagation path information of the adjacent edges of each node is recorded.

[0071] In the later stage of propagation, a residual propagation is performed on the propagation representation of stage two to obtain the propagation representation of stage three, and the propagation path record set is output.

[0072] Based on the propagation path record set, structural dependency paths and anomaly sensitive paths are extracted, and propagation operations are performed separately to obtain structural dependency propagation representation sets and anomaly sensitive propagation representation sets. Based on the weighted fusion of health score vector and key level vector, a dual-path fusion state representation set is generated, and local state difference and cross-layer difference are calculated. Residual fusion is performed to obtain the industrial equipment state perception vector set.

[0073] This invention performs sliding time window statistics on the set of state-aware vectors for industrial equipment, outputs a set of abnormal devices based on a deviation score threshold, and generates a set of propagation tracing paths by combining this with a set of propagation path records. By recording the propagation connections and their contributions between nodes during multi-stage propagation, this invention ultimately generates a set of propagation tracing paths. This set of propagation tracing paths can intuitively reveal the propagation links of abnormal states in the industrial equipment network, enabling the location of the abnormal source, prediction of the abnormal impact range, and explanation of causal relationships. Maintenance personnel can quickly determine the root cause of the fault and the affected equipment based on the set of propagation tracing paths, thereby improving the interpretability and practicality of the industrial equipment state-awareness method.

[0074] In this embodiment, the industrial equipment operation data includes temperature data, vibration data, current data, power data, and communication data. The preprocessing steps include time alignment, noise reduction, and normalization of the operation data. The three types of adjacency matrices include process flow adjacency matrix, energy flow adjacency matrix, and communication link adjacency matrix.

[0075] In this embodiment, the steps of calculating the health score vector and the critical level vector based on operational data include:

[0076] The average temperature and temperature fluctuation amplitude are calculated from the temperature data; the root mean square value of vibration and frequency domain energy are calculated from the vibration data; the average current and peak current are calculated from the current data; the active power and power factor are calculated from the power data; and the packet loss rate and delay rate are calculated from the communication data. The calculation results are combined into a health score vector.

[0077] The in-degree and out-degree of each node are calculated in the process flow adjacency matrix, the energy transfer intensity of each node is calculated in the energy flow adjacency matrix, and the connection stability of each node is calculated in the communication link adjacency matrix. The in-degree, out-degree, energy transfer intensity, and connection stability are combined into a key level vector.

[0078] In a specific embodiment of the present invention, the process of constructing the key level vector includes the following steps:

[0079] Based on the process flow adjacency matrix, the in-degree and out-degree of each node are calculated. The in-degree represents the number of process dependencies received by the node, and the out-degree represents the number of process dependencies output by the node. The sum of the in-degree and out-degree is used to characterize the coupling strength of the node in the process chain.

[0080] Based on the energy flow adjacency matrix, the energy transmission intensity of each node is calculated. The energy transmission intensity is obtained by weighted summation of the power transmission values ​​of the energy flow edges connected to the node. The larger the value, the stronger the criticality of the node in the energy transmission process.

[0081] Based on the adjacency matrix of the communication link, the connection stability of each node is calculated. The connection stability is obtained by combining link delay, packet loss rate and link availability. The lower the delay, the lower the packet loss rate and the higher the availability, the higher the communication stability of the node.

[0082] The in-degree and out-degree, energy transmission intensity, and connection stability are combined according to the node index to form a key level vector, which is used to characterize the comprehensive importance of the node in terms of technology, energy, and communication.

[0083] In this embodiment, the generation process of the stage-one propagation representation in the improved APPNP propagation structure includes: performing row-wise normalization on the fused adjacency matrix to obtain a normalized fused adjacency matrix; setting a quantile threshold q based on the health score vector, selecting nodes with health score values ​​lower than q as high-risk nodes, and generating a risk gating vector composed of 0s and 1s according to the node index; wherein, the health score vector is a numerical vector calculated from temperature, vibration, current, power, and communication data, and each element in the vector corresponds to the health score value of a node; setting a quantile threshold p based on the criticality level vector, selecting nodes with criticality level values ​​higher than p as critical nodes, and generating a criticality gating vector composed of 0s and 1s according to the node index; wherein, criticality... The rank vector is a numerical vector calculated based on the in-degree and out-degree of the process flow adjacency matrix, the energy transmission intensity of the energy flow adjacency matrix, and the connection stability of the communication link adjacency matrix. The critical rank value is the value corresponding to each node in the critical rank vector. Gating is applied to the normalized fused adjacency matrix, retaining edges where the source node's risk gating vector is 1 and the target node's critical gating vector is 1, while setting other edges to zero, resulting in the stage-one gated adjacency matrix. The initial state input is then subjected to a neighborhood aggregation operation with the stage-one gated adjacency matrix, and the first neighborhood aggregation result is obtained by row-weighted summation. Finally, the propagation coefficient α1 and the state prior vector are linearly combined to generate the seeding and reinjection result. The specific process of the first neighborhood aggregation operation is as follows:

[0084] The stage-1 gated adjacency matrix is ​​row-normalized so that the sum of the weights of the edges connecting each node is 1, ensuring that the propagation results are numerically stable. The normalized adjacency matrix is ​​used to guide the transmission of information in the neighborhood of a node.

[0085] For each target node, iterate through all its neighbor nodes retained in the stage-1 gated adjacency matrix, extract the feature representation of the neighbor nodes in the initial state input, and perform weighted summation according to the normalized edge weights to obtain the first neighborhood aggregation result of the target node. This weighted summation operation reflects the state information received by the target node from its direct neighbors during the propagation process.

[0086] The first neighborhood aggregation result of the target node is weighted and added to its initial state value in the state prior vector. The weighting coefficient is controlled by the propagation ratio α1. This operation combines the propagation information with the initial prior information, avoids excessive smoothing caused by the propagation process relying entirely on the features of neighboring nodes, and maintains the state features of the node itself.

[0087] Finally, after all nodes have completed the above weighted calculations, the aggregated output matrix of Phase 1 is formed, which serves as the initial result of the Phase 1 propagation representation.

[0088] The seeding and reinjection results are processed using neighborhood contrast gain processing. The difference between each node and its next-order neighborhood mean in the stage-one gated adjacency matrix is ​​calculated. Positive difference intervals are amplified by a gain coefficient g1, while non-positive difference intervals remain unchanged, resulting in the amplified result. The specific process of neighborhood contrast gain processing is as follows:

[0089] For each node, extract all first-order neighbor nodes from the stage-1 gated adjacency matrix, calculate the average value of these neighbor nodes in the seeding and back-injection results, and obtain the neighborhood mean of this node.

[0090] The difference between the value of this node in the seeding and injection results and the mean of its neighborhood is obtained. The neighborhood comparison difference is used to measure the degree of deviation of this node from the overall state of its neighborhood.

[0091] The neighborhood comparison difference of all nodes is divided into intervals. When the difference is positive, it indicates that the state of this node is higher than the neighborhood mean. At this time, the seeding and reinjection results of the node are amplified by the gain coefficient g1. When the difference is less than or equal to zero, it indicates that the state of the node is not higher than the neighborhood mean. At this time, the original seeding and reinjection results are kept unchanged.

[0092] After the above processing is completed, the values ​​of all nodes constitute the amplified propagation output. The amplified propagation output retains the characteristic responses of nodes that are significantly higher in the neighborhood background, so that abnormal nodes are highlighted in the subsequent propagation representation.

[0093] The amplified result is subjected to interval pruning and normalization. Items exceeding the upper limit are taken from the upper limit, and items below the lower limit are taken from the lower limit. The result is linearly scaled to the range [0,1] within a fixed interval to obtain the stage-1 propagation representation. The propagation path is recorded based on the stage-1 gated adjacency matrix and the first neighborhood aggregation result. The recording rule is to calculate the actual contribution value to the target node for each retained edge and filter out edges with contribution values ​​lower than the threshold τ1 to obtain the stage-1 propagation path record set.

[0094] In this embodiment, the generation process of the stage 2 propagation representation in the improved APPNP propagation structure includes:

[0095] The phase-one propagation representation is analyzed sequentially by sliding time window. The mean μ and standard deviation σ of each node within the window are calculated. The difference d between the current value of the node and the mean μ in the phase-one propagation representation is calculated to obtain the amplitude of node state change.

[0096] A nonlinear attenuation factor is constructed based on the magnitude of node state abrupt changes. This nonlinear attenuation factor is determined by the basic attenuation coefficient β, the exponential attenuation function, and the magnitude correction function. When the difference d is greater than zero, the attenuation factor is calculated using the following formula: ;

[0097] When the difference d is less than zero, the formula for calculating the attenuation factor is: ;

[0098] Generate a dynamic decay vector for each node;

[0099] The second neighborhood aggregation operation is performed on the propagation representation of the first stage and the fused adjacency matrix. The propagation values ​​of all neighboring nodes are collected for the target node, and the weighted sum is calculated according to the normalized adjacency edge weights to obtain the second neighborhood aggregation result.

[0100] The second neighborhood aggregation result is multiplied element-wise with the dynamic decay vector to obtain the decay-controlled propagation output;

[0101] A structural balance term is superimposed on the attenuation-controlled propagation output. The structural balance term is generated by multiplying the key level vector with the corresponding value in the fusion adjacency matrix to obtain the compensated propagation result.

[0102] The compensated propagation result is linearly weighted and fused with the state prior vector to output the stage 2 propagation representation.

[0103] In the Phase 2 propagation representation, the weighted contribution value of each edge to the target node during the neighborhood aggregation process is calculated. The edges are sorted according to the weighted contribution value, and only the top k% of the edges are retained as valid paths, forming a set of Phase 2 propagation path records.

[0104] In this embodiment, the generation process of the stage three propagation representation in the improved APPNP propagation structure includes:

[0105] Element-wise difference is performed between the propagation representation of stage two and the propagation representation of stage one to obtain the cross-stage residual vector;

[0106] For stage two propagation, the difference Δ between the mean μt and the current value vt is calculated using a sliding time window, and a long-term memory factor is constructed using the following formula: ;

[0107] In the fused adjacency matrix, only stable edges that appear in both the propagation path record set of stage one and the propagation path record set of stage two are retained to obtain a stable adjacency matrix.

[0108] The third neighborhood aggregation operation is performed on the second-stage propagation representation and the stable adjacency matrix. The values ​​of the stable neighbor nodes are collected for the target node, and the values ​​are weighted and summed according to the corresponding values ​​in the stable adjacency matrix to obtain the third neighborhood aggregation result.

[0109] The third neighborhood aggregation result is multiplied element-wise with the long-term memory factor, and the cross-stage residual vector is added to obtain the retention compensation propagation output. The retention compensation propagation output is then weighted and fused with the state prior vector to output the stage three propagation representation.

[0110] In the third-stage propagation representation, the propagation path is recorded. The recording rule is to retain only the edges that appear in all three stages of the propagation path record set, thus forming the third-stage propagation path record set.

[0111] In this embodiment, the process of extracting structural dependency paths and abnormal sensitive paths based on the propagation path record set and performing propagation operations respectively includes:

[0112] In the set of propagation path records in stage three, edges that exist simultaneously in the process flow adjacency matrix, energy flow adjacency matrix, and communication chain adjacency matrix are selected to construct a set of structurally dependent paths;

[0113] In the set of propagation path records in stage three, by combining the state mutation amplitude sequence, the edges associated with nodes whose mutation amplitude is greater than the threshold δ are selected to construct the set of abnormal sensitive paths.

[0114] The neighborhood aggregation operation is performed on the adjacency submatrix corresponding to the propagation representation of the third stage and the set of structural dependency paths. For each target node, the values ​​are collected from the nodes directly connected to the target node in the set of structural dependency paths, and a weighted sum is performed according to the values ​​in the adjacency submatrix to obtain the structural dependency propagation result vector.

[0115] The neighbor aggregation operation is performed on the adjacency submatrix corresponding to the stage 3 propagation representation and the set of abnormal sensitive paths. For each node, the values ​​are collected from the abnormal sensitive neighbor nodes of the node and the values ​​in the adjacency submatrix are weighted and summed to obtain the abnormal sensitive propagation result vector.

[0116] The structure dependency propagation result vector is normalized to generate a set of structure dependency propagation representations;

[0117] The anomaly-sensitive propagation result vector is normalized to generate an anomaly-sensitive propagation representation set.

[0118] In this embodiment, the process of calculating the local state difference and cross-layer difference and performing residual fusion to obtain the industrial equipment state perception vector set includes:

[0119] In the dual-path fusion state representation set, for each target node, its first-order neighbor nodes in the fusion adjacency matrix are extracted, and the difference between the target node value and the mean of the values ​​of all first-order neighbor nodes is calculated to form a local state difference vector.

[0120] The propagation representations of stage one, stage two, and stage three are compared layer by layer, and the numerical differences of the same node in adjacent propagation stages are calculated to form a cross-layer difference vector.

[0121] The local state difference vector and the cross-layer difference vector are concatenated according to the node index and normalized to obtain the set of state difference feature vectors.

[0122] The set of state difference feature vectors is added element by element to the set of dual-path fusion state representations to form a preliminary residual fusion result;

[0123] A residual amplification function is applied to the preliminary residual fusion result. When the local state difference is positive, it is amplified by the amplification factor g2. When the local state difference is zero or negative, it remains unchanged to obtain the amplified residual fusion result.

[0124] The amplified residual fusion result is normalized and numerically pruned, and the numerical values ​​are mapped to the interval [0,1] and output as a set of industrial equipment state perception vectors.

[0125] In the improved APPNP propagation structure of this invention, the specific process of layer-by-layer comparison is as follows:

[0126] First, for each node, extract its values ​​in the propagation representation of stage one, stage two, and stage three in sequence to form the cross-stage value sequence of that node.

[0127] Secondly, calculate the difference between nodes in adjacent propagation stages, that is, subtract the value of stage one from the value of stage two, and subtract the value of stage two from the value of stage three, to obtain the difference between stage one and stage two and the difference between stage two and stage three, respectively.

[0128] Furthermore, the above difference values ​​are used as the initial results of cross-layer difference to represent the dynamic change trend of nodes between different propagation stages.

[0129] Furthermore, in order to enhance the identification effect of mutation nodes, the numerical values ​​of cross-layer difference are standardized. The mean value of the propagation stage where the node is located is used as the benchmark. The difference result is divided by the mean value to obtain the relative difference value, so as to maintain comparability between propagation stages with different numerical scales.

[0130] Finally, the relative difference values ​​of all nodes are arranged according to their node indices to form a cross-layer difference vector, which is used to concatenate with the local state difference vector and perform residual fusion.

[0131] In this invention, the specific process of residual fusion is as follows:

[0132] First, the local state difference vector and the cross-layer difference vector are concatenated according to the node index to form a set of difference feature vectors. The local state difference reflects the instantaneous anomaly of a node in its neighborhood, while the cross-layer difference reflects the dynamic changes of the node between propagation stages.

[0133] Secondly, the set of differential feature vectors is added element-wise to the set of dual-path fusion state representations to obtain the preliminary residual fusion result. This step ensures that the state information of a node not only includes its global impact in path propagation, but also retains residual information of local offsets and stage changes.

[0134] Next, a residual amplification function is applied to the preliminary residual fusion result. When the local state difference is positive, it indicates that the value of the node is significantly higher than the neighborhood mean, and the fusion result of that node is multiplied by an amplification factor g2. When the local state difference is zero or negative, it indicates that the value of the node is not higher than the neighborhood mean, and the original value is kept unchanged. This processing ensures that the characteristic responses of potentially abnormal nodes are highlighted in the result, while normal nodes remain stable.

[0135] Subsequently, the amplified residual fusion results are truncated to limit all values ​​to between the set upper and lower limits to prevent extreme values ​​from distorting the overall results.

[0136] Finally, the clipped results are normalized to map the values ​​to the [0,1] interval, resulting in a set of industrial equipment state perception vectors. This vector set can represent the state level of all nodes on a unified numerical scale, including both global path propagation features and local and cross-layer difference features, providing input for subsequent anomaly detection and source tracing analysis.

[0137] In this embodiment, the process of outputting the abnormal equipment set based on the deviation score threshold includes: performing sliding time window statistics on the industrial equipment state perception vector set, calculating the mean and standard deviation of each node within the window, generating a standardized deviation score vector, marking nodes in the standardized deviation score vector with values ​​greater than a set threshold as abnormal nodes, and outputting the abnormal equipment set composed of the abnormal nodes.

[0138] Example 1:

[0139] To verify the feasibility of this invention in practice, it was applied to the monitoring of the operational status of a group of key equipment in a large-scale industrial production scenario. In this scenario, the production system includes multiple motors, pumps, sensors, and control nodes. There are complex process flow relationships, energy transmission relationships, and communication chain relationships between the equipment. Traditional status monitoring methods rely solely on single sensor thresholds for anomaly detection, which often results in false alarms and missed alarms, making it difficult to locate the source of anomaly propagation. Especially in environments with a large number of devices and diverse data dimensions, anomalies often propagate in a coupled manner, and conventional methods cannot reveal their causal links.

[0140] In this scenario, temperature, vibration, current, power, and communication data of the equipment were collected. Through time alignment, denoising, and normalization, standardized operational data was formed. Further, process flow adjacency matrices, energy flow adjacency matrices, and communication chain adjacency matrices were constructed. A fused adjacency matrix was formed through gated weighted fusion. Combined with the operational data, health score vectors and criticality level vectors were generated. In the improved APPNP propagation structure, risk enhancement propagation was first performed, amplifying nodes with lower health scores during propagation. Then, nonlinear decay propagation was performed, using a dynamic decay factor to control the amplitude of state mutations and avoid unstable diffusion. Finally, retention compensation propagation was performed, introducing long-term memory factors and cross-stage residual compensation to ensure the long-term influence of critical nodes. After three stages of propagation, a final path record set was formed, and reliable propagation links were retained through path consistency screening.

[0141] In subsequent processing, structurally dependent paths and anomaly-sensitive paths are extracted from the path record set and propagation calculations are performed separately to obtain structurally dependent propagation representation sets and anomaly-sensitive propagation representation sets. These are then fused based on health scores and critical levels with weighted averages. Subsequently, local state differences and cross-layer differences are calculated, and residual fusion is performed to finally obtain a set of industrial equipment state perception vectors. Based on this set, a sliding time window is used to calculate the standardized deviation score. By setting a threshold, an abnormal equipment set is output. Combined with the path record set, a propagation tracing path set is generated for source tracing analysis and decision support.

[0142] In practical applications, this invention enables comprehensive monitoring of operating status. Compared with traditional threshold detection methods, this invention can reduce false alarm and false negative rates and provide anomaly propagation links. In a group of tested devices, a motor's vibration value increased due to bearing abnormality. Traditional methods can only detect the motor abnormality but cannot explain the source of current fluctuations in downstream pumps. This invention reveals, through a set of propagation tracing paths, that the motor abnormality is transmitted to downstream pumps via energy flow adjacency relationships, further affecting sensor nodes in the communication chain, thus providing a clear anomaly propagation link.

[0143] Experimental data shows that the present invention outperforms traditional methods in terms of accuracy, recall, and F1 score. The comparison table shows that traditional methods have lower accuracy in detecting anomalies and insufficient anomaly tracing capabilities; the present invention not only accurately identifies abnormal devices but also provides causal path information. Within the monitoring period, the present invention can identify potential device anomalies in advance, reducing unplanned downtime and improving operational efficiency.

[0144] Table 1: Performance Comparison of Industrial Equipment Condition Sensing Methods

[0145] ;

[0146] As shown in Table 1, the traditional threshold method exhibits the lowest performance in terms of accuracy, recall, and F1 score, with an accuracy of 82.4%, a recall of 74.6%, and an F1 score of 78.3%. While this method achieves basic anomaly detection, its over-reliance on a single threshold setting results in an average false alarm rate of 12.7% and a false negative rate of 14.5%, indicating insufficient stability in anomaly detection. Furthermore, it fails to provide traceability information, limiting its application value in complex device networks.

[0147] The single graph neural network-based method offers performance improvements over the traditional thresholding method, increasing detection accuracy to 88.1%, recall to 83.5%, and F1 score to 85.7%. Meanwhile, the average false alarm rate and false negative rate decrease to 9.6% and 11.1%, respectively. This method can model the topological relationships between devices to some extent, thus improving detection capabilities. However, the interpretability of the tracing path remains weak, and the average detection latency is 4.8 seconds, which still has certain limitations in real-time performance.

[0148] The proposed industrial equipment state perception method based on the improved APPNP exhibits superior performance, achieving a detection accuracy of 95.7%, a recall of 92.4%, and an F1 score of 94.0%, all significantly outperforming comparative methods. The average false alarm rate and false negative rate are reduced to 4.3% and 5.1%, respectively, demonstrating more reliable and stable anomaly detection. Regarding interpretability, the invention outputs a set of propagation tracing paths through a three-stage propagation structure and path recording mechanism, providing strong interpretability and effectively revealing the anomaly propagation chain. Simultaneously, the average detection latency is reduced to 3.1 seconds, showcasing high real-time performance and applicability. These results demonstrate that the invention not only achieves significant advantages in accuracy and stability but also possesses outstanding value in interpretability and real-time performance, providing a more comprehensive solution for anomaly monitoring and tracing in industrial equipment.

[0149] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for industrial equipment state perception based on the PageRank graph calculation algorithm, characterized in that, Includes the following steps: Collect operational data from industrial equipment, including temperature data, vibration data, current data, power data, and communication data. The preprocessing constructs a set of industrial equipment nodes and three types of adjacency matrices, including a process flow adjacency matrix, an energy flow adjacency matrix, and a communication link adjacency matrix. The three types of adjacency matrices reflect the topological relationships of industrial equipment in three dimensions: process flow, energy transmission, and communication connection. The value of each element in the matrix is ​​used to indicate whether there is a connection between nodes. If there is a connection, it is a non-zero value; if there is no connection, it is a zero value. Based on the operational data, calculate the health score vector and the key level vector, normalize them to form the state prior vector, and concatenate them with the node feature vector set to obtain the initial state input. Calculate the gate weights for the three types of adjacency matrices, and perform weighted fusion according to the gate weights to obtain the fused adjacency matrix; The improved APPNP propagation structure combines the initial state input with the fused adjacency matrix input to amplify the propagation intensity of abnormally high-risk nodes in the initial propagation stage, generating a stage-one propagation representation. During the middle of the propagation, a decay factor is applied to the propagation representation of stage one to obtain the propagation representation of stage two, and the propagation path information of the adjacent edges of each node is recorded. In the later stage of propagation, a residual propagation is performed on the propagation representation of stage two to obtain the propagation representation of stage three, and the propagation path record set is output. Based on the propagation path record set, structural dependency paths and anomaly sensitive paths are extracted, and propagation operations are performed separately to obtain structural dependency propagation representation sets and anomaly sensitive propagation representation sets. Based on the weighted fusion of health score vector and key level vector, a dual-path fusion state representation set is generated, and local state difference and cross-layer difference are calculated. Residual fusion is performed to obtain the industrial equipment state perception vector set. A sliding time window is used to statistically analyze the set of state perception vectors of industrial equipment, and a set of abnormal equipment is output based on the deviation score threshold. The set of propagation path records is then combined to generate a set of propagation tracing paths.

2. The industrial equipment state perception method based on the PageRank graph calculation algorithm according to claim 1, characterized in that, The industrial equipment operating data includes temperature data, vibration data, current data, power data, and communication data. The preprocessing steps include time alignment, noise reduction, and normalization of the operating data.

3. The industrial equipment state perception method based on the PageRank graph calculation algorithm according to claim 2, characterized in that, The steps for calculating the health score vector and key level vector based on operational data include: The average temperature and temperature fluctuation amplitude are calculated from the temperature data; the root mean square value of vibration and frequency domain energy are calculated from the vibration data; the average current and peak current are calculated from the current data; the active power and power factor are calculated from the power data; and the packet loss rate and delay rate are calculated from the communication data. The calculation results are combined into a health score vector. The in-degree and out-degree of each node are calculated in the process flow adjacency matrix, the energy transfer intensity of each node is calculated in the energy flow adjacency matrix, and the connection stability of each node is calculated in the communication link adjacency matrix. The in-degree, out-degree, energy transfer intensity, and connection stability are combined into a key level vector.

4. The industrial equipment state perception method based on the PageRank graph calculation algorithm according to claim 3, characterized in that, The generation process of the stage-one propagation representation in the improved APPNP propagation structure includes: performing row-wise normalization on the fused adjacency matrix to obtain a normalized fused adjacency matrix; setting a quantile threshold q based on the health score vector, selecting nodes with health scores lower than q as high-risk nodes, and generating a risk gating vector composed of 0 and 1 according to the node index; setting a quantile threshold p based on the critical level vector, selecting nodes with critical level values ​​higher than p as critical nodes, and generating a critical gating vector composed of 0 and 1 according to the node index; applying gating to the normalized fused adjacency matrix, retaining the edges where the risk gating vector corresponding to the source node is 1 and the critical gating vector corresponding to the target node is 1, and setting other edges to zero to obtain a stage-one gated adjacency matrix; performing neighborhood aggregation operation on the initial state input and the stage-one gated adjacency matrix, performing row-weighted summation to obtain the first neighborhood aggregation result, and generating the seeding and back-injection result by linear combination of the propagation coefficient α1 and the state prior vector; The neighbor comparison gain processing is performed on the seeding and injection results. The difference between each node and the mean of the next-order neighborhood in the stage-1 gated adjacency matrix is ​​calculated. The positive difference interval is amplified by the gain coefficient g1, while the non-positive difference interval remains unchanged to obtain the amplified result. The amplified result is subjected to interval pruning and normalization. Items exceeding the upper limit are taken from the upper limit, and items below the lower limit are taken from the lower limit. The result is linearly scaled to the range [0,1] within a fixed interval to obtain the stage-1 propagation representation. The propagation path is recorded based on the stage-1 gated adjacency matrix and the first neighborhood aggregation result. The recording rule is to calculate the actual contribution value to the target node for each retained edge and filter out edges with contribution values ​​lower than the threshold τ1 to obtain the stage-1 propagation path record set.

5. The industrial equipment state perception method based on the PageRank graph calculation algorithm according to claim 4, characterized in that, The generation process of the phase 2 propagation representation in the improved APPNP propagation structure includes: The phase-one propagation representation is analyzed sequentially by sliding time window. The mean μ and standard deviation σ of each node within the window are calculated. The difference d between the current value of the node and the mean μ in the phase-one propagation representation is calculated to obtain the amplitude of node state change. A nonlinear attenuation factor is constructed based on the magnitude of node state abrupt changes. This nonlinear attenuation factor is determined by the basic attenuation coefficient β, the exponential attenuation function, and the magnitude correction function. When the difference d is greater than zero, the attenuation factor is calculated using the following formula: ; When the difference d is less than zero, the formula for calculating the attenuation factor is: ; Generate a dynamic decay vector for each node; The second neighborhood aggregation operation is performed on the propagation representation of the first stage and the fused adjacency matrix. The propagation values ​​of all neighboring nodes are collected for the target node, and the weighted sum is calculated according to the normalized adjacency edge weights to obtain the second neighborhood aggregation result. The second neighborhood aggregation result is multiplied element-wise with the dynamic decay vector to obtain the decay-controlled propagation output; A structural balance term is superimposed on the attenuation-controlled propagation output. The structural balance term is generated by multiplying the key level vector with the corresponding value in the fusion adjacency matrix to obtain the compensated propagation result. The compensated propagation result is linearly weighted and fused with the state prior vector to output the stage 2 propagation representation. In the Phase 2 propagation representation, the weighted contribution value of each edge to the target node during the neighborhood aggregation process is calculated. The edges are sorted according to the weighted contribution value, and only the top k% of the edges are retained as valid paths, forming a set of Phase 2 propagation path records.

6. The industrial equipment state perception method based on the PageRank graph calculation algorithm according to claim 5, characterized in that, The generation process of the phase three propagation representation in the improved APPNP propagation structure includes: Element-wise difference is performed between the propagation representation of stage two and the propagation representation of stage one to obtain the cross-stage residual vector; For stage two propagation, the difference Δ between the mean μt and the current value vt is calculated using a sliding time window, and a long-term memory factor is constructed using the following formula: ; In the fused adjacency matrix, only stable edges that appear in both the propagation path record set of stage one and the propagation path record set of stage two are retained to obtain a stable adjacency matrix. The third neighborhood aggregation operation is performed on the second-stage propagation representation and the stable adjacency matrix. The values ​​of the stable neighbor nodes are collected for the target node, and the values ​​are weighted and summed according to the corresponding values ​​in the stable adjacency matrix to obtain the third neighborhood aggregation result. The third neighborhood aggregation result is multiplied element-wise with the long-term memory factor, and the cross-stage residual vector is added to obtain the retention compensation propagation output. The retention compensation propagation output is then weighted and fused with the state prior vector to output the stage three propagation representation. In the third-stage propagation representation, the propagation path is recorded. The recording rule is to retain only the edges that appear in all three stages of the propagation path record set, thus forming the third-stage propagation path record set.

7. The industrial equipment state perception method based on the PageRank graph calculation algorithm according to claim 6, characterized in that, The process of extracting structural dependency paths and abnormally sensitive paths based on the propagation path record set, and performing propagation operations on them respectively, includes: In the set of propagation path records in stage three, edges that exist simultaneously in the process flow adjacency matrix, energy flow adjacency matrix, and communication chain adjacency matrix are selected to construct a set of structurally dependent paths; In the set of propagation path records in stage three, combined with the state mutation amplitude sequence, the edges associated with nodes whose mutation amplitude is greater than the threshold δ are selected to construct an abnormal sensitive path set. The neighborhood aggregation operation is performed on the adjacency submatrix corresponding to the propagation representation of the third stage and the set of structural dependency paths. For each target node, the values ​​are collected from the nodes directly connected to the target node in the set of structural dependency paths, and a weighted sum is performed according to the values ​​in the adjacency submatrix to obtain the structural dependency propagation result vector. The neighbor aggregation operation is performed on the adjacency submatrix corresponding to the stage 3 propagation representation and the set of abnormal sensitive paths. For each node, the values ​​are collected from the abnormal sensitive neighbor nodes of the node and the values ​​in the adjacency submatrix are weighted and summed to obtain the abnormal sensitive propagation result vector. The structure dependency propagation result vector is normalized to generate a set of structure dependency propagation representations; The anomaly-sensitive propagation result vector is normalized to generate an anomaly-sensitive propagation representation set.

8. The industrial equipment state perception method based on the PageRank graph calculation algorithm according to claim 7, characterized in that, The process of calculating the local state difference and cross-layer difference and performing residual fusion to obtain the industrial equipment state perception vector set includes: In the dual-path fusion state representation set, for each target node, extract the first-order neighbor nodes of the target node in the fusion adjacency matrix, calculate the difference between the target node value and the mean value of all first-order neighbor nodes, and form a local state difference vector. The propagation representations of stage one, stage two, and stage three are compared layer by layer, and the numerical differences of the same node in adjacent propagation stages are calculated to form a cross-layer difference vector. The local state difference vector and the cross-layer difference vector are concatenated according to the node index and normalized to obtain the set of state difference feature vectors. The set of state difference feature vectors is added element by element to the set of dual-path fusion state representations to form a preliminary residual fusion result; A residual amplification function is applied to the preliminary residual fusion result. When the local state difference is positive, it is amplified by the amplification factor g2. When the local state difference is zero or negative, it remains unchanged to obtain the amplified residual fusion result. The amplified residual fusion result is normalized and numerically pruned, and the numerical values ​​are mapped to the interval [0,1] and output as a set of industrial equipment state perception vectors.

9. The industrial equipment state perception method based on the PageRank graph calculation algorithm according to claim 8, characterized in that, The process of outputting the abnormal equipment set based on the deviation score threshold includes: performing sliding time window statistics on the industrial equipment state perception vector set, calculating the mean and standard deviation of each node within the window, generating a standardized deviation score vector, marking nodes in the standardized deviation score vector with values ​​greater than a set threshold as abnormal nodes, and outputting the abnormal equipment set composed of the abnormal nodes.

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