Adaptive graph diagnosis method and system fusing structure perception and dynamic propagation

Abstract

The invention discloses an adaptive graph diagnosis method and system fusing structure perception and dynamic propagation. The method comprises the following steps: collecting a vibration acceleration signal in a typical fault state; dividing the vibration acceleration signal data into a plurality of time windows, taking sampling data of each time window as node features of a graph, and constructing graph structure data; based on the graph structure data, utilizing a structure perception similarity modeling mechanism to measure the structure similarity between the nodes, and dynamically adjusting a feature aggregation strategy; performing multi-layer feature propagation and fusion on the feature aggregation strategy by using a local adaptive residual feature propagation mechanism; and inputting the fused node representation into a classification module, and outputting a corresponding fault type to realize intelligent fault diagnosis. While the calculation efficiency is maintained, the recognition capability of weak fault features in complex industrial signals is remarkably improved. Effective representation, feature enhancement and fault type high-precision classification of the multi-source time sequence signals are realized.

Description

Technical Field

[0001] The present invention relates to the field of industrial intelligent monitoring and graph neural network modeling, and particularly to an adaptive graph diagnosis method and system integrating structure perception and dynamic propagation. Background Art

[0002] With the wide deployment of high-end equipment in key fields such as aerospace, intelligent manufacturing, power energy, and rail transit, its core operating components (such as bearings, gears, rotors, etc.) are in a long-term state of high load, high speed, and complex environmental interference, and are prone to generate weak or even non-linear early fault signals. To ensure the stable operation of the equipment and extend its service life, how to achieve high-precision, strong-robustness, and low-latency fault identification and health assessment of key components has become a core technical issue in intelligent manufacturing and equipment operation and maintenance.

[0003] Traditional data-driven diagnosis methods mainly rely on machine learning algorithms such as support vector machines and decision trees, and rely on manually constructed features, making it difficult to adapt to the complexity of signal patterns brought about by changes in working conditions. In recent years, deep learning technology has developed rapidly, and methods such as convolutional neural networks (CNNs) and recurrent neural networks (RNNs) have been widely applied to the field of fault diagnosis. CNNs are good at extracting local spatial features from raw vibration or acoustic signals, while RNNs are more suitable for capturing temporal change trends. However, CNNs are limited by the convolutional receptive field and are difficult to capture long-distance dependencies across windows. RNNs have problems such as gradient disappearance and long training time in long sequence modeling.

[0004] As an emerging non-Euclidean data processing tool, graph neural networks (GNNs) show powerful representation capabilities in complex system modeling by modeling the topological relationships and attribute interactions between nodes. Especially in industrial scenarios, sensor data usually has characteristics such as heterogeneity, multi-source, and structural non-uniformity. The introduction of GNNs provides a new modeling idea for such problems. However, existing GNN methods generally face homogeneous graph structures, that is, it is assumed that nodes are of the same type and neighbor labels are consistent, making it difficult to cope with the real-world scenarios of changing equipment working conditions and heterogeneous signal sources. In addition, when the number of layers of mainstream GNNs is deepened, node features tend to be consistent in multiple rounds of aggregation, resulting in the "over-smoothing" phenomenon, losing key fault difference information and seriously affecting the model performance.

[0005] Therefore, there is an urgent need to design a new intelligent diagnosis framework for heterogeneous graph structures, taking into account multi-frequency feature fusion and the effectiveness of deep propagation, so as to break through the application bottleneck of existing methods. Summary of the Invention

[0006] In view of the above existing problems, the present invention is proposed.

[0007] To solve the above technical problems, the present invention provides the following technical solution: an adaptive graph diagnosis method that integrates structure perception and dynamic propagation, including: collecting vibration acceleration signals under typical fault conditions;

[0008] Dividing the vibration acceleration signal data into multiple time windows, using the sampled data of each time window as the node features of the graph, and constructing graph structure data;

[0009] Based on the graph structure data, using a structure-aware similarity modeling mechanism to measure the structural similarity between nodes, and dynamically adjusting the feature aggregation strategy;

[0010] Using a local adaptive residual feature propagation mechanism to perform multi-layer feature propagation and fusion on the feature aggregation strategy;

[0011] Inputting the fused node representation into the classification module, outputting the corresponding fault type, and realizing intelligent fault diagnosis.

[0012] As a preferred solution of the adaptive graph diagnosis method that integrates structure perception and dynamic propagation according to the present invention, wherein: the typical fault conditions include but are not limited to, healthy state, outer ring fault, inner ring fault, rolling element fault, compound fault.

[0013] As a preferred solution of the adaptive graph diagnosis method that integrates structure perception and dynamic propagation according to the present invention, wherein: the graph structure data consists of a feature matrix and an adjacency matrix;

[0014] In the construction stage of the feature matrix, the time series signal is sampled through a specified time window, and the feature vectors of each time window are stacked into columns to obtain the feature matrix;

[0015] The adjacency matrix is jointly composed of time-order edges and similarity edges; the time-order edges include, if two nodes are adjacent in the time series, it is recorded as 1; otherwise, it is recorded as 0;

[0016] The similarity edges include, calculating the similarity of the feature vectors of any two nodes; if the similarity reaches the preset value, it is recorded as 1; otherwise, it is recorded as 0.

[0017] As a preferred solution of the adaptive graph diagnosis method that integrates structure perception and dynamic propagation according to the present invention, wherein: the structure-aware similarity modeling mechanism includes, in a sensor network, node ν i The structural perception similarity between a node and its neighbor nodes is expressed as:

[0018] Wherein, d ij Represents node ν i And neighbor node ν jFeature similarity measurement between denotes the neighbor set of node ν i ; the neighbor nodes are the nodes directly connected to node ν i ;

[0019] Taking the square term of the structure-aware similarity as an additional feature input, the nonlinear relationship is modeled through a multi-layer perceptron:

[0020]

[0021] where ψ' i represents the nonlinear expression result of the structure-aware similarity weight of the node; MLP sasm represents the multi-layer perceptron used in the structure-aware similarity modeling module for nonlinearly mapping the input features.

[0022] As a preferred solution of the adaptive graph diagnosis method that fuses structure awareness and dynamic propagation according to the present invention, wherein: the local adaptive residual feature propagation mechanism includes removing the inter-layer nonlinear operation and introducing a residual information propagation strategy in the standard GNN structure:

[0023] The node representation of the first layer is: H (1) = LARFP (1) (F, X) = FX;

[0024] The node representation of the l-th layer is:

[0025] where X is the original input feature; γ ∈ [0, 1] represents a hyperparameter; represents a graph filter, representing the topological structure of the graph through a normalized adjacency matrix; l represents the index of the layer; LARFP (l) represents the local adaptive residual feature propagation operation of the l-th layer; represents the index of the layer before the l-th layer; represents the normalized degree matrix; represents the normalized adjacency matrix;

[0026] Applying a low-pass filter and a high-pass filter respectively, and obtaining the feature representation of the l-th layer:

[0027]

[0028] Projecting the d-dimensional feature into the z-dimensional feature space through a learnable weight matrix:

[0029]

[0030] where is a learnable weight matrix; Represents a real matrix space of d rows and c columns; Represents the low-frequency information of the l-th layer; Represents the high-frequency information of the l-th layer; F L Represents a low-pass filter; F G Represents a high-pass graph filter; ξ ∈ [0, 1] is a hyperparameter; I represents the identity matrix; Represents a non-linear transformation function; Represents the low-frequency feature of the l-th layer after projection transformation; Represents the high-frequency feature of the l-th layer after projection transformation; A represents the adjacency matrix; D represents the degree matrix;

[0031] During the dimension transformation process, an additional transformation of the original feature X is introduced:

[0032]

[0033] Among them, Is a learnable weight matrix; Represents the original feature after projection transformation.

[0034] As a preferred solution of the adaptive graph diagnosis method that combines structure perception and dynamic propagation according to the present invention, wherein: the multi-layer feature propagation and fusion includes Performing multi-order fusion to obtain the final node representation;

[0035] Node v i Fusion weight calculation: [λ I , λ L , λ G = MLP λ ([ψ', ψ' 2 )

[0036] Among them, Represents the fusion weight of the node in the initial layer feature; Represents the fusion weight of the node in the low-pass filtering layer feature; Represents the fusion weight of the node in the high-pass filtering layer feature; MLP λ Represents the multi-layer perceptron for calculating λ; ψ' = [ψ'1, ψ'2,..., ψ' n ; n represents the number of nodes; Represents the n-dimensional real space;

[0037] For the l-th layer, the fusion representation of all nodes is:

[0038]

[0039] Among them, ⊙ represents element-wise multiplication, Represents λI the \(l\)-th column of denotes \(\lambda\) L the \(l\)-th column of denotes \(\lambda\) G the \(l\)-th column of.

[0040] As a preferred solution of the adaptive graph diagnosis method that fuses structure perception and dynamic propagation according to the present invention, wherein: the fused node representation includes, after multi-layer feature fusion, splicing the features of each layer to form the final node representation:

[0041]

[0042] Wherein, is a learnable output weight matrix, \(C\) represents the number of fault categories, \(L\) represents the number of layers, \(z\) represents the transformed dimension, and \(\parallel\) represents the feature splicing operation; \(Z\) (L) is the final node representation of the \(L\)-th layer.

[0043] An adaptive graph diagnosis system that fuses structure perception and dynamic propagation using the method according to the present invention, characterized in that: an acquisition module that acquires vibration acceleration signals in a typical fault state; a processing module that divides the vibration acceleration signal data into multiple time windows, and uses the sampled data of each time window as the node features of the graph to construct graph structure data; an adjustment module that, based on the graph structure data, uses a structure perception similarity modeling mechanism to measure the structural similarity between nodes and dynamically adjusts the feature aggregation strategy; a calculation module that uses a local adaptive residual feature propagation mechanism to perform multi-layer feature propagation and fusion on the feature aggregation strategy; a classification module that inputs the fused node representation and outputs the corresponding fault type to achieve intelligent fault diagnosis.

[0044] A computer device, comprising: a memory and a processor; the memory stores a computer program, wherein: when the processor executes the computer program, the steps of the method described in any one of the present invention are implemented.

[0045] A computer-readable storage medium, on which a computer program is stored, wherein: when the computer program is executed by a processor, the steps of the method described in any one of the present invention are implemented.

[0046] Advantages of the present invention: The adaptive graph diagnosis method integrating structure perception and dynamic propagation provided by the present invention is based on a graph neural network, constructs a hybrid graph structure including time-dependent edges and similarity edges, and combines structure-aware similarity modeling and multi-frequency feature residual propagation mechanism to significantly improve the recognition ability of weak fault features in complex industrial signals while maintaining computational efficiency. Aiming at the data heterogeneity, structural complexity in the sensor signals during the operation of high-end industrial equipment and the over-smoothing problem in the training of deep models, an adaptive heterogeneous graph intelligent diagnosis method integrating structure perception and dynamic residual propagation is provided to achieve effective representation, feature enhancement and high-precision classification of fault types for multi-source time series signals. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present invention, and those of ordinary skill in the art can obtain other drawings according to these drawings without creative efforts.

[0048] Figure 1 The overall flowchart of an adaptive graph diagnosis method integrating structure perception and dynamic propagation provided for the first embodiment of the present invention;

[0049] Figure 2 The comparison results of the time consumed for model training in an adaptive graph diagnosis method integrating structure perception and dynamic propagation provided for the second embodiment of the present invention;

[0050] Figure 3 The performance of GCN and the proposed method under different network layers in an adaptive graph diagnosis method integrating structure perception and dynamic propagation provided for the second embodiment of the present invention;

[0051] Figure 4 The verification results of the model ablation experiment in an adaptive graph diagnosis method integrating structure perception and dynamic propagation provided for the second embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0052] To make the above objects, features and advantages of the present invention more obvious and understandable, the specific embodiments of the present invention will be described in detail below with reference to the drawings of the specification. Obviously, the described embodiments are some embodiments of the present invention, rather than all embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0053] Example 1, refer to Figure 1, which is an embodiment of the present invention, provides an adaptive graph diagnosis method that integrates structure perception and dynamic propagation, including:

[0054] Step 1: Conduct a vibration test experiment on the typical faults of bearings, which are the most commonly used in high-end equipment rotating machinery, and collect the vibration acceleration signals in typical fault states.

[0055] The acceleration signals of the bearings include the vibration acceleration signals in various typical fault states such as healthy state, outer ring fault, inner ring fault, rolling element fault, and compound fault.

[0056] Step 2: Divide the vibration acceleration signal data into multiple time windows and construct graph structure data. The graph structure data consists of a feature matrix and an adjacency matrix, and the adjacency matrix is jointly composed of time-order edges and similarity-based edges.

[0057] A method for constructing graph data based on a hybrid strategy of time series and similarity measurement aims to effectively convert time series signals into graph data to meet the requirements of fault diagnosis tasks. This method mainly includes two key steps: feature matrix construction and adjacency matrix construction. First, in the construction stage of the feature matrix, the time series signal is sampled through a specified time window, and the sampled data of each time window is used as the node feature of the graph. Assume the length of the time series signal is L and it is divided into several time windows, where the data within each window is expressed as where d is the feature dimension of each time window, n is the number of nodes, and n = L / d.

[0058] Therefore, the feature matrix is constructed by stacking the feature vectors of each time window into columns, providing an effective representation of the temporal evolution of the signal.

[0059] The construction of the adjacency matrix is a crucial step in graph data processing, which is defined as the connection relationship between nodes in the graph. In this method, the construction of the adjacency matrix is divided into two major steps, namely, time-order edges and similarity edges, to better capture the temporal dependencies and global patterns in the signal. Time-order edges mainly capture local short-term dependencies by modeling the temporal continuity. Specifically, it is stipulated that the n nodes in each type of fault data are connected in sequence, that is, the i-th node forms an edge connection with the i + 1-th node to construct the local order structure of the graph. Mathematically, the adjacency matrix of the time-order edge can be expressed as A ts , where each node i is connected to node i + 1, and the elements in the matrix satisfy:

[0060]

[0061] i represents the current node, and j represents any node.

[0062] Through this chronological construction method, the graph data can effectively capture the local evolution and short-term dependencies of time series signals.

[0063] Compared with local time dependencies, long-range dependencies and periodic features in bearing vibration signals often generate similar vibration patterns between different time points of the signal, and this information is crucial for fault diagnosis. Therefore, during the construction of the adjacency matrix, a similarity-based edge construction method is introduced to reveal the dependencies between remote nodes by calculating the similarity between nodes. Given any two nodes ν i and node ν j , calculate the similarity measure S(i, j) of their feature vectors, and cosine similarity or Euclidean distance can be used for calculation.

[0064] By setting a similarity threshold θ, when S(i, j) > θ, an edge connection is formed between node i and node j. Mathematically, the adjacency matrix A sim (i, j) is expressed as:

[0065]

[0066] Generally speaking, this hybrid strategy first effectively models the local continuity of the signal using chronological edges, capturing the gradual evolution process of the vibration signal, which is of great significance for identifying sudden faults. Secondly, by introducing similarity edges, it can effectively identify long-range dependencies and global patterns in the signal. Especially during the long-term operation of the bearing, periodic fault patterns often have similarities across time steps, and simple chronological modeling often fails to reveal these long-range dependencies. The hybrid strategy combines the two, providing richer and more accurate data input for the application of GNN in fault diagnosis, and thus comprehensively improving the performance of the GNN model in bearing fault diagnosis, especially when dealing with complex bearing vibration signals with periodic and non-linear characteristics.

[0067] Step 3: Based on the graph structure data, use the Structural-Aware Similarity Modeling (SASM) mechanism to measure the structural similarity between nodes and dynamically adjust the feature aggregation strategy.

[0068] The Structural-Aware Similarity Modeling (SASM) method is used to measure the similarity of different nodes in the topological structure and adaptively adjust the feature fusion method during the information propagation process. Specifically, SASM is mainly used to measure the consistency of the target node and its neighborhood in the feature space, so as to provide guidance for subsequent GNN propagation. Suppose in a sensor network, the structural-aware similarity between node ν i and its neighbor nodes is expressed as:

[0069]

[0070] where d ij = S(i,j) represents the feature similarity metric between node v i and its neighbor node v j ; represents the neighbor set of node v i ; the neighbor nodes are the nodes directly connected to node ν i .

[0071] The structure-aware similarity reflects the information consistency of nodes in the local topological structure, that is, whether their neighborhoods have similar feature patterns. In a homogeneous environment, nodes with higher structural similarity can usually directly rely on neighbor information to enhance their own features. In a heterogeneous environment, however, there may be significant differences in the features between neighbors. Therefore, it is necessary to optimize the information propagation strategy to reduce the impact of incorrect information. For example, in a fault diagnosis task, if a certain node in a sensor network records an abnormal vibration signal while most of its neighbor nodes are in a normal state, directly aggregating neighbor information by traditional GNNs may weaken the abnormal features of this node, thus affecting the final classification accuracy. Therefore, in a heterogeneous environment, SASM can effectively help the model determine when to enhance neighborhood features and when to rely more on its own information.

[0072] In addition, to further enhance the expressive power of the structure-aware similarity, we introduce a non-linear mapping to capture the high-order information of the feature distribution. Specifically, the squared term of the structure-aware similarity is used as an additional feature input, and the non-linear relationship is modeled through a multi-layer perceptron:

[0073]

[0074] where ψ' i represents the non-linear expression result of the structure-aware similarity weight of the node; MLP sasm represents the multi-layer perceptron used in the structure-aware similarity modeling module for non-linearly mapping the input features.

[0075] This improvement enables the structure-aware similarity to not only measure the first-order similarity between a node and its neighbors but also encode the variance information of the similarity distribution, enhancing its ability to distinguish different types of nodes in complex environments. For example, in traditional similarity calculation methods, if a certain node v1 has two neighbors v2 and v3, and d 12 = 0, d 13 = 1, then its calculated structure similarity value ψ1 may be the same as that of another node v4 (whose neighbors all have similar features), resulting in the inability to effectively distinguish different types of nodes. However, through the non-linear mapping, ψ'i , the model can identify the distribution characteristics of different neighborhoods, and then more accurately model the local structural differences between nodes. Through SASM, we can classify the structures of nodes before information propagation, enabling isomorphic nodes to preferentially receive neighborhood information, while heterogeneous nodes rely more on their own features, thereby optimizing the feature propagation strategy in the fault diagnosis task.

[0076] Step 4: Based on the Locally Adaptive Residual Feature Propagation (LARFP), perform multi-layer feature propagation and fusion to balance the propagation of high-frequency and low-frequency information and alleviate the over-smoothing phenomenon in deep graph neural networks.

[0077] It should be noted that the structure-aware similarity modeling mechanism is the first step. Its main task is to dynamically adjust the information aggregation strategy by measuring the structural similarity between nodes. The core goal of this step is to optimize feature aggregation based on the feature similarity between nodes and their neighbors, thereby improving the model's discrimination ability for different node features. This similarity modeling must be completed before feature aggregation because only through this process can a reasonable similarity-based feature representation be provided for subsequent feature propagation.

[0078] Immediately afterwards, the locally adaptive residual feature propagation mechanism is applied to the multi-layer feature propagation and fusion stage after the similarity modeling is completed. The role of the LARFP mechanism is to guide the flow of information through the residual path during the information propagation process, avoid the over-smoothing problem existing in traditional GNN models, and further enhance the effect of multi-layer information fusion. Only after the similarity modeling can the LARFP mechanism perform effective feature propagation and fusion based on the correct features.

[0079] Therefore, the order of these two steps is determined by their respective functions: similarity modeling provides important structural information for feature propagation, while feature propagation performs multi-level feature fusion based on this information. Reversing the order may lead to a lack of basis for the feature aggregation strategy, affecting the performance and stability of the entire model.

[0080] In the fault diagnosis task, the multi-layer feature propagation of sensor data is the key to improving the model performance. However, traditional GNNs mainly rely on the simple aggregation of inter-layer information, which may lead to the loss of important fault features and further cause the over-smoothing problem in deep models. To ensure the full interaction of information between different layers and avoid the loss of representational ability of the model during deep propagation, we propose a new feature propagation strategy - locally adaptive-guided residual feature propagation, which can ensure the effectiveness of each layer of information and enhance the learning ability for complex industrial signals.

[0081] In standard GNN architectures (such as GCN, GAT), the basic form of information propagation is as follows:

[0082]

[0083] where H (l) is the node representation of the l-th layer, W (l) is the trainable parameter matrix, is the non-linear activation function, F is the graph filter, and the topological structure of the graph is represented by the normalized adjacency matrix

[0084] Inspired by SGC, we remove the inter-layer non-linear operations and design a new residual information propagation strategy: in the standard GNN architecture, remove the inter-layer non-linear operations and introduce the residual information propagation strategy:

[0085] The node representation of the first layer is: H (1) = LARFP (1) (F, X) = FX.

[0086] The node representation of the l-th layer is:

[0087] where X is the original input feature; γ ∈ [0, 1] represents the hyperparameter; represents the graph filter, and the topological structure of the graph is represented by the normalized adjacency matrix; l represents the layer index; LARFP (l) represents the local adaptive residual feature propagation operation of the l-th layer; represents the layer index before the l-th layer; represents the normalized degree matrix; represents the normalized adjacency matrix; the core idea of this method is that each layer contains a certain proportion of the original input information (1 - γ)X to ensure that the model does not lose the original features during deep propagation; the cumulative information of the previous l - 1 layers is introduced in a residual manner so that the information of different layers can be comprehensively utilized, so that the messages of different layers can maintain sufficient distinctiveness without causing information over-smoothing. Through the above node representation update strategy, the LARFP mechanism can dynamically maintain the input information and avoid the problem of information decay during deep propagation.

[0088] ​In the traditional GCN structure, GNN mainly uses the filter after adjacency matrix normalization for information propagation. However, this method usually only focuses on low-pass filtering and ignores high-frequency information. In the industrial fault diagnosis scenario, low-pass information helps capture global patterns, while high-pass information can enhance the ability to capture abnormal signals. Therefore, only using low-pass information may miss important fault features. Therefore, in the LARFP mechanism, enhanced filters are introduced to achieve the joint propagation of low-pass and high-frequency information.

[0089] Apply low-pass filtering and high-pass filters respectively, and obtain the feature representation of the l-th layer:

[0090]

[0091] After the extraction of low-pass and high-frequency information is completed, the model needs to further transform these features to reduce the computational complexity, improve the information expression ability, and ensure that different types of features can be reasonably optimized during the fusion process. During the GNN propagation process, low-pass filtering and high-pass filtering The generated features are still in the high-dimensional space (d-dimensional), and directly using high-dimensional features for node classification has a large computational amount and may lead to redundant information propagation. Therefore, we first project the d-dimensional features into a more compact z-dimensional feature space through a learnable weight matrix, so that it can perform information fusion more efficiently. The specific calculation is as follows:

[0092]

[0093] where, is a learnable weight matrix, whose role is to reduce the feature dimension while retaining the most discriminative low-pass and high-frequency information; represents a real matrix space of d rows and c columns; represents the low-frequency information of the l-th layer; represents the high-frequency information of the l-th layer; F L represents the low-pass filter; F G represents the high-pass graph filter; ξ ∈ [0, 1] is a hyperparameter; I represents the identity matrix; represents the non-linear transformation function; represents the low-frequency feature of the l-th layer after projection transformation; represents the high-frequency feature of the l-th layer after projection transformation; A represents the adjacency matrix; D represents the degree matrix.

[0094] During the dimension transformation process, an additional transformation of the original feature X is introduced to ensure that the model does not completely lose the initial state information during information propagation:

[0095]

[0096] Among them, is a learnable weight matrix; represents the original features after projection transformation. Finally, for perform multi-level fusion to obtain the final node representation.

[0097] In GNN, the fusion of features is an important step to improve the accuracy and robustness of the model. Especially in fault diagnosis tasks, the features between nodes may have significant differences, which makes the feature fusion of different layers crucial. Traditional feature fusion methods usually use fixed weighting strategies. However, in complex fault diagnosis tasks, the similarity between nodes will vary with different tasks. Therefore, designing an adaptive feature fusion mechanism based on structure-aware similarity becomes an effective solution. This method dynamically adjusts the fusion weights of features at different levels by combining the structure-aware similarity of nodes, thus achieving excellent classification effects in both homogeneous and heterogeneous graphs.

[0098] To effectively fuse features at different levels, we first need to calculate an adaptive fusion weight for each node, that is, the contribution degree of the features of each node between different layers. This fusion weight is calculated based on structure-aware similarity and can dynamically adjust the influence of different layers according to the local structural features of the nodes. Specifically, for node v i the calculation of the fusion weight:

[0099] [λ I λ L , λ G = MLP λ ([ψ', ψ' 2 )

[0100] Among them, represents the fusion weight of the features of the node in the initial layer; represents the fusion weight of the features of the node in the low-pass filtering layer; represents the fusion weight of the features of the node in the high-pass filtering layer; MLP λ represents the multi-layer perceptron for calculating λ; ψ' = [ψ'1, ψ'2,..., ψ' n ; n represents the number of nodes; represents the n-dimensional real number space.

[0101] In this way, the final representation of the node can combine low-pass and high-pass information and adaptively adjust the weights according to the structure-aware similarity, so as to effectively fuse the features of different layers.

[0102] After calculating the fusion weights of each node, we further fuse the multi-layer features. During the feature fusion process of the l-th layer, we first extract the features of node v i to obtain the low-frequency and high-frequency representations. Then, the final representation Z i of node v (l) is calculated through the weighted low-pass and high-pass features:

[0103]

[0104] where ⊙ represents element-wise multiplication, represents the l-th column of λ I , represents the l-th column of λ L , represents the l-th column of λ G . This dynamic fusion weight mechanism based on node structure-aware similarity ensures that the performance of nodes at different feature levels can be better integrated, thus improving the classification ability of the model under multi-fault modes.

[0105] Step Five: Input the finally fused node representation into the classification module to output the corresponding fault type and achieve intelligent fault diagnosis.

[0106] After multi-layer feature fusion, we concatenate the features of each layer to form the final node representation. This representation is further passed to the output layer for classification prediction. The concatenated form of the final node representation is:

[0107]

[0108] where is the learnable output weight matrix, C represents the number of fault categories, L represents the number of layers, z represents the transformed dimension, ∥ represents the feature concatenation operation; Z (L) is the final node representation of the L-th layer.

[0109] During this process, the final representation of the node can reflect multi-level and different-scale feature information, greatly enhancing the ability of fault mode recognition. Therefore, the proposed multi-layer feature fusion mechanism based on structure-aware similarity dynamically adjusts the weights of feature fusion by introducing local structure-aware similarity, ensuring the effective fusion of information in the multi-layer propagation of nodes. This method can flexibly adapt to the structural changes of homogeneous and heterogeneous graphs, significantly improving the classification accuracy in the fault diagnosis task.

[0110] On the other hand, this embodiment also provides an adaptive graph diagnosis system that fuses structure awareness and dynamic propagation, which includes:

[0111] A collection module that collects vibration acceleration signals in typical fault states; a processing module that divides the vibration acceleration signal data into multiple time windows, uses the sampling data of each time window as the node features of a graph, and constructs graph-structured data; an adjustment module that, based on the graph-structured data, uses a structure-aware similarity modeling mechanism to measure the structural similarity between nodes and dynamically adjusts the feature aggregation strategy; a calculation module that uses a local adaptive residual feature propagation mechanism to perform multi-layer feature propagation and fusion on the feature aggregation strategy; a classification module that inputs the fused node representations and outputs the corresponding fault types to achieve intelligent fault diagnosis.

[0112] If the above functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of this technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present invention. The aforementioned storage medium includes: USB flash drives, mobile hard disks, read-only memories (ROM, Read-Only Memory), random access memories (RAM, Random Access Memory), magnetic disks, or optical discs, etc., which can store program codes.

[0113] The logic and / or steps represented in the flowchart or described in other ways herein, for example, can be considered as a definite sequence list of executable instructions for implementing logical functions, and can be specifically implemented in any computer-readable medium for use by an instruction execution system, apparatus, or device (such as a computer-based system, a system including a processor, or other systems that can fetch instructions from the instruction execution system, apparatus, or device and execute the instructions), or in combination with these instruction execution systems, apparatus, or devices. For the purposes of this specification, a "computer-readable medium" can be any device that can contain, store, communicate, propagate, or transmit a program for use by or in combination with an instruction execution system, apparatus, or device.

[0114] More specific examples (a non-exhaustive list) of computer-readable media include the following: electrical connections (electronic devices) having one or more wirings, portable computer disk cartridges (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber devices, and portable compact disc read-only memory (CDROM). Additionally, the computer-readable media can even be paper or other suitable media on which the program can be printed, since the program can be obtained electronically, for example, by optically scanning the paper or other media, followed by editing, interpretation, or other suitable processing as necessary, and then stored in a computer memory.

[0115] It should be understood that the various parts of the present invention can be implemented by hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, any one or a combination of the following techniques well known in the art can be used: discrete logic circuits having logic gate circuits for implementing logical functions on data signals, application specific integrated circuits having suitable combinational logic gate circuits, programmable gate arrays (PGA), field programmable gate arrays (FPGA), etc.

[0116] Example 2, referring to Figures 2 - 4 ..., is an embodiment of the present invention, which provides an adaptive graph diagnosis method that fuses structure perception and dynamic propagation. To verify the beneficial effects of the present invention, scientific demonstration is carried out through economic benefit calculation and simulation experiments.

[0117] To ensure the effectiveness of model training and the comparability of experimental results, unified data preprocessing and parameter configuration are carried out in this paper. First, for the original vibration signals, sliding time windows with a fixed length of 1024 are used for segmentation. The data of each time window is regarded as the input feature of a single node, and it is ensured that each fault type contains 100 node samples to ensure the balance of class distribution. All node data are standardized before being input into the model to improve the convergence speed and stability of model training. The dataset is divided into a training set, a validation set, and a test set according to a ratio of 6:2:2, which are used for model parameter training, hyperparameter optimization, and final performance evaluation respectively. The model training uses the Adam optimizer, with the initial learning rate set to 0.001, the maximum number of iterations to 200, the batch size to 64, and the early stopping strategy is enabled to prevent overfitting.

[0118] To comprehensively verify the effectiveness and advancement of the proposed model in the fault diagnosis task, this paper designs a systematic comparative experiment covering multiple mainstream model algorithms to ensure the scientificity and rigor of the comparison results. Specifically, three representative comparative algorithms are selected for the experiment: (1) The classic model based on non-graph structure - Multi-Layer Perceptron (MLP), which only utilizes the node's own feature information and cannot capture topological dependencies, serves as the benchmark for non-graph structure modeling; (2) Classic GNN models based on homogeneous graphs, including Graph Convolutional Network (GCN) and Graph Attention Network (GAT). These methods can achieve local feature aggregation based on graph structure information, but generally suffer from problems such as over-reliance on low-pass filtering and insufficient adaptability to heterogeneous graph structures; (3) Graph learning models optimized for heterogeneous graphs and complex topological structures, such as MixHop, GPRGNN, and H2GCN. These methods have been improved in aspects such as multi-order feature aggregation and information propagation mechanisms, aiming to enhance the representation ability for complex fault patterns. The comparison models cover multiple levels from traditional single-node feature learning to complex heterogeneous graph modeling, and the verification baseline settings are sufficient and widely representative.

[0119] Table 1 Test results of the baseline algorithms and the proposed method on different datasets

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[0121]

[0122] The experimental results are shown in Table 1. The classification accuracy of the proposed model on the three typical datasets is significantly better than that of the existing methods, demonstrating good generalization ability and robustness. Specifically, on the DIRG_Bearing dataset, the proposed model achieved the highest classification accuracy of 97.62%, significantly exceeding the existing optimal models GPRGNN and H2GCN. In the other two datasets, the proposed method also performed outstandingly, further verifying its strong adaptability and robustness in different data environments. These experimental results fully prove the effectiveness and wide applicability of the method in this paper under different complex working conditions and multi-modal sensing data. From the overall performance of the comparison models, the traditional MLP model has a low classification accuracy on the three datasets because it does not consider the topological structure and dependence relationship between nodes. Although classical GNNs such as GCN and GAT can effectively aggregate information between nodes using the graph structure, their information propagation process mainly relies on the low-pass filtering mechanism, resulting in limited performance under heterogeneous graphs and complex fault modes. In particular, although GAT introduces the attention mechanism to enhance the feature expression ability, there are still problems with insufficient generalization ability when dealing with heterogeneous data and complex working conditions. Improved models such as MixHop and GPRGNN have improved the modeling ability of complex graph structures to a certain extent by introducing multi-scale aggregation and higher-order neighbor information. However, there are still limitations in heterogeneous graph information fusion and alleviating the over-smoothing problem. H2GCN has been optimized in the ability to process heterogeneous graphs, but due to its imperfect deep feature fusion mechanism, the improvement of the model in feature expression ability and classification accuracy is limited. In contrast, the model proposed in this paper effectively alleviates the over-smoothing and information loss problems in traditional GNN models by introducing LARFP and the multi-layer feature fusion mechanism based on structure-aware similarity. At the same time, SASM further enhances the model's adaptability to heterogeneous graph data, enabling the model to maintain high classification accuracy and robustness in various complex working conditions and multi-modal signal environments. The comprehensive experimental results show that the method in this paper not only outperforms the existing mainstream models in terms of classification accuracy, but also has stronger generalization ability and complex environment adaptability, fully demonstrating its application potential in the field of high-end equipment health monitoring and intelligent fault diagnosis.

[0123] Comparative analysis of training time:

[0124] In practical industrial applications such as fault diagnosis and health monitoring, the computational efficiency of a model is one of the important indicators to measure its practicality. Especially in the tasks of real-time monitoring and dynamic regulation of high-end equipment, the model not only needs to have high classification accuracy, but also should have fast training and inference speeds to meet the system's requirements for high responsiveness and low latency. Therefore, this paper further compares and analyzes the performance of the proposed method and typical baseline models in terms of training time, focusing on their computational efficiency and engineering application potential. In the experimental settings, all models are trained on the same dataset, hyperparameter configuration, and hardware environment to ensure the fairness and comparability of the results. The specific results of the training time are as Figure 2 shown. From the overall performance of the training time, the classic GCN and GAT take 3.28 seconds and 4.16 seconds respectively. Both of these types of models use layer-by-layer convolution or adjacency information aggregation operations, and perform non-linear activation or attention weight calculation at each layer, resulting in a relatively high computational complexity. Especially when dealing with large-scale graph data, the training efficiency is further reduced.

[0125] In contrast, by removing multi-layer non-linear activation operations and only retaining the graph filter and linear transformation, SGC greatly simplifies the computational process and achieves the optimal training time of 0.93 seconds. However, although the SGC model has advantages in computational efficiency, its overly simplified feature propagation mechanism limits its ability to model complex patterns and heterogeneous data, making it difficult to meet the fault identification needs in multi-modal complex scenarios. Based on the above methods, the model proposed in this paper controls the computational complexity of the network while enhancing the model's expressive ability and discriminative ability by introducing LARFP and a multi-layer feature fusion mechanism of structure-aware similarity. Experimental data shows that the training time of the proposed model is 1.42 seconds, significantly better than mainstream GNN models such as GCN and GAT, and close to the lightweight SGC model. This result indicates that the proposed method effectively alleviates the computational bottleneck commonly existing in deep graph structure models while improving the robustness and generalization ability of the model, achieving efficient training under a complex model architecture. This comparative analysis also shows that the proposed model takes into account both the feature modeling ability and computational efficiency, and has good real-time performance and engineering application potential in tasks such as heterogeneous graph structure processing of multi-modal sensing data and dynamic fault classification under complex working conditions. It is especially suitable for large-scale deployment in high-end equipment health monitoring systems, intelligent manufacturing equipment, and industrial Internet of Things environments, meeting the multiple requirements for model accuracy, computational efficiency, and resource consumption in practical applications.

[0126] Analysis of the over-smoothing problem:

[0127] Over-Smoothing is a common problem in deep GNN models during the process of multi-layer stacking. As the number of network layers increases, node features gradually tend to be homogenized, resulting in a significant reduction in the distinguishability between nodes and seriously affecting the classification performance of the model. Especially in complex working conditions such as high-end equipment fault diagnosis, fault features usually manifest as small but critical differences, and the over-smoothing phenomenon of traditional GNN models further exacerbates the confusion of fault types and reduces the practicality and reliability of the diagnostic system. Therefore, alleviating the over-smoothing problem has become the key to enhancing the depth ability and generalization performance of the model.

[0128] To verify the effectiveness of the proposed method in alleviating the over-smoothing phenomenon, this paper selects the classic GCN as a comparison baseline and evaluates the change trend of the classification accuracy of GCN and the proposed method under different layer settings. The experimental results are as Figure 3 shown. It can be observed that the GCN model can still maintain a certain classification accuracy when it is in the shallow layer (2 - 3 layers). However, as the number of model layers increases, the classification performance of GCN drops rapidly. When the number of layers increases to 10 layers, the accuracy rate has dropped to 57.36%. This indicates that under the deep structure, the node representations of the GCN model tend to be homogenized, making it difficult to retain effective feature information, the over-smoothing problem is significant, and the model's expressive ability is greatly weakened.

[0129] In contrast, the proposed model still maintains a high classification performance under the multi-layer structure. Under the shallow structure, the model accuracy steadily increases with the increase in the number of layers, and the 5-layer model reaches the best accuracy rate of 97.62%. Even when the number of layers is further increased, the model can still maintain a high performance. Even under the extremely deep structures of 9 layers and 10 layers, the accuracy rate still remains at a high level without obvious performance degradation. This fully shows that the proposed method effectively alleviates the information loss and feature over-smoothing problems in the deep stacking process of traditional GNNs through the LARFP and the multi-layer feature fusion mechanism based on structure-aware similarity. The locally similar-guided residual path dynamically adjusts the feature transfer and the proportion of residual information between different layers, ensuring that the initial features of the nodes can be retained during the deep propagation process, while the structure-aware multi-layer fusion realizes the balance of high-frequency and low-frequency information, further enhancing the discrimination ability of node representations. Therefore, the model proposed in this paper not only has excellent classification ability under the shallow network structure, but also effectively avoids the over-smoothing phenomenon in the deep network architecture, demonstrating stronger feature expression ability and model robustness.

[0130] Analysis of the Plug-and-Play Module Capability of SASM:

[0131] To further verify the generality and effectiveness of the proposed SASM module, a series of plug-and-play experiments are designed in this section. The SASM module is integrated into the current mainstream GNN models (GPRGNN and H2GCN) and the main model architecture proposed in this paper respectively, and comprehensive comparative analysis is carried out on three typical datasets. From the analysis of the overall experimental results, as a lightweight plug-and-play unit, the SASM module can significantly improve the classification performance of different models and maintain consistent performance gains under different datasets and working conditions. Specifically, after introducing the SASM module, the classification accuracies of the GPRGNN model on three different datasets are increased from 94.12%, 90.11% and 87.27% to 95.57%, 91.43% and 88.06% respectively. Similarly, the performance of the H2GCN model is slightly improved after integrating the SASM module. This result demonstrates the wide adaptability and effectiveness of the SASM module in different GNN architectures. By introducing a structure-aware similarity evaluation mechanism, this module dynamically measures and adjusts the information propagation weights between nodes, which can effectively alleviate the information confusion problem under heterogeneous graph data and improve the discriminative ability of node representations. At the same time, the SASM module is lightweight in structure, has low computational overhead, does not introduce an obvious training burden, and has excellent pluggability and scalability, making it suitable for the rapid integration of various GNN architectures.

[0132] Ablation experiment:

[0133] To comprehensively verify the effectiveness and necessity of the key modules in the model proposed in this paper, ablation experiments are designed and implemented in this section, and different components of the model are systematically analyzed. The focus is on investigating the influence of the SASM module and the local self-adaptive guided residual feature propagation mechanism on the overall model performance. By conducting comparative experiments with individual modules removed while keeping other parameters and experimental conditions the same, their roles in the model's classification accuracy, feature representation ability, and adaptability to complex working conditions are deeply analyzed. The specific experimental results are as Figure 4 shown. First, after removing the SASM module, the model no longer has a dynamic information propagation mechanism based on local structure-aware similarity and cannot adaptively adjust the information fusion strategy according to the structural heterogeneity between nodes and their neighbors. The experimental results show that in the absence of the SASM module, the classification performance of the model drops to 96.14%, 93.36% and 91.59% respectively. Although the overall performance is still higher than that of some existing comparative models, it still decreases compared with the complete model. This result verifies the important role of the SASM module in enhancing the discriminability of node features and improving the classification accuracy of heterogeneous graph data. By dynamically adjusting the weights, SASM makes the model more flexible and robust when processing multi-modal sensor data under complex working conditions, and significantly alleviates the problem of class confusion in the node information propagation process.

[0134] Secondly, when the LARFP module is removed, the model lacks an effective residual information regulation mechanism, resulting in a weakened information transmission ability and a decreased feature expression ability in the deep network structure. Especially when the number of GNN layers increases, the traditional information aggregation method often causes serious over-smoothing, leading to the attenuation of node representation ability. Experimental data shows that after removing the LARFP module, the accuracy of the model on three typical datasets is reduced by 1.04%, 0.96%, and 1.06% compared to the complete model. This phenomenon indicates that the LARFP module, by introducing a residual path guided by local similarity, not only effectively preserves the original feature information of nodes but also enhances the deep feature fusion ability of the model, thus still being able to maintain strong node discrimination and feature expression ability under the high-level graph structure and alleviating the performance degradation problem caused by over-smoothing.

[0135] Based on the comprehensive ablation experiment results, the complete model integrates two key modules, SASM and LARFP, and achieves the best classification accuracy. Compared with the models with a single module removed, the complete model shows more excellent performance under multi-dataset and multi-condition scenarios. This fully verifies the scientificity and rationality of the design of the two modules and also indicates that their synergistic effect in the model is significant. SASM is responsible for accurately modeling the structural similarity between nodes and improving the quality of information fusion under heterogeneous graph data, while LARFP enhances the deep representation ability and robustness of the model through residual information guidance and multi-layer information regulation. The synergistic effect of the two enables the proposed model to not only have excellent classification performance but also good generalization ability and engineering application potential.

[0136] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the spirit and scope of the technical solutions of the present invention, and they should all be covered within the scope of the claims of the present invention.

Claims

1. An adaptive graph diagnosis method that integrates structure perception and dynamic propagation, characterized in that Including: Collect vibration acceleration signals in typical fault states; Divide the vibration acceleration signal data into multiple time windows, and use the sampling data of each time window as the node features of the graph to construct graph structure data; Based on the graph structure data, use the structure-aware similarity modeling mechanism to measure the structural similarity between nodes and dynamically adjust the feature aggregation strategy; Use the local adaptive residual feature propagation mechanism to perform multi-layer feature propagation and fusion on the feature aggregation strategy; Input the fused node representation into the classification module, output the corresponding fault type, and realize intelligent fault diagnosis.

2. The adaptive graph diagnosis method integrating structure perception and dynamic propagation according to claim 1, characterized in that: The typical fault states include, but are not limited to, healthy state, outer race fault, inner race fault, rolling element fault, and compound fault.

3. The adaptive graph diagnosis method that integrates structure perception and dynamic propagation according to claim 2, wherein: The graph structure data consists of a feature matrix and an adjacency matrix; In the construction stage of the feature matrix, the time series signal is sampled through a specified time window, and the feature vectors of each time window are stacked into columns to obtain the feature matrix; The adjacency matrix is jointly composed of time-order edges and similarity edges; the time-order edges include that if two nodes are adjacent in the time series, they are recorded as 1; Conversely, it is recorded as 0; The similarity edges include calculating the similarity of the feature vectors of any two nodes; if the similarity reaches the preset value, it is recorded as 1; Conversely, it is recorded as 0.

4. The adaptive graph diagnosis method that integrates structure perception and dynamic propagation according to claim 3, wherein: The structure-aware similarity modeling mechanism includes, in a sensor network, the structure-aware similarity between node ν i and its neighbor nodes is expressed as: Among them, d ij represents the feature similarity measure i between node v j and its neighbor node v represents the neighbor set of node v i ; the neighbor nodes are the nodes directly connected to node v i ​ Take the square term of the structure-aware similarity as an additional feature input and model the non-linear relationship through a multi-layer perceptron: Among them, ψ' i represents the non-linear expression result of the structure-aware similarity weight of the node; MLP sasm represents the multi-layer perceptron used in the structure-aware similarity modeling module for non-linearly mapping the input features.

5. The adaptive graph diagnosis method that integrates structure perception and dynamic propagation according to claim 4, characterized in that: The local adaptive residual feature propagation mechanism includes removing the inter-layer non-linear operation in the standard GNN structure and introducing a residual information propagation strategy: The nodes of the first layer are represented as: H (1) = LARFP (1) (F, X) = FX; The nodes of the l-th layer are represented as: Among them, X is the original input feature; γ ∈ [0, 1] represents the hyperparameter; represents the graph filter, which represents the topological structure of the graph by normalizing the adjacency matrix; l represents the index of the layer; LARFP (l) represents the local adaptive residual feature propagation operation of the l-th layer; represents the index of the layer before the l-th layer; represents the normalized degree matrix; represents the normalized adjacency matrix; Apply a low-pass filter and a high-pass filter respectively and obtain the feature representation of the l-th layer: Project the d-dimensional feature into the z-dimensional feature space through a learnable weight matrix: Among them, is a learnable weight matrix; represents a space of real matrices with d rows and c columns; represents the low-frequency information of the l-th layer; represents the high-frequency information of the l-th layer; F L represents a low-pass filter; F G represents a high-pass graph filter; ξ ∈ [0, 1] is a hyperparameter; I represents the identity matrix; represents a non-linear transformation function; represents the low-frequency feature of the l-th layer after projection transformation; represents the high-frequency feature of the l-th layer after projection transformation; A represents the adjacency matrix; D represents the degree matrix; During the dimension transformation process, an additional transformation of the original feature X is introduced: Among them, is a learnable weight matrix; represents the original features after projection transformation.

6. The adaptive graph diagnosis method integrating structure perception and dynamic propagation according to claim 5, characterized in that: The multi-layer feature propagation and fusion includes performing multi-order fusion on to obtain the final node representation; Node v i Calculation of the fusion weight: [λ I , λ L , λ G = MLP λ ([ψ', ψ' 2 ) Among them, represents the fusion weight of the node in the initial layer feature; represents the fusion weight of the node in the low-pass filtering layer feature; represents the fusion weight of the node in the high-pass filtering layer feature; MLP λ represents the multi-layer perceptron for calculating λ; ψ' = [ψ'1, ψ'2,..., ψ' n ; n represents the number of nodes; represents the n-dimensional real number space; For the l-th layer, the fused representation of all nodes is: where, ⊙ represents element-wise multiplication, represents the l-th column of λ I , represents the l-th column of λ L , represents the l-th column of λ G .

7. The adaptive graph diagnosis method that integrates structure perception and dynamic propagation according to claim 6, wherein: The fused node representation includes that after multi-layer feature fusion, the features of each layer are concatenated to form the final node representation: Among them, is a learnable output weight matrix, C represents the number of fault categories, L represents the number of layers, z represents the transformed dimension, and || represents the feature concatenation operation; Z (L) is the final node representation of the L-th layer.

8. An adaptive graph diagnosis system that integrates structure perception and dynamic propagation using the method according to any one of claims 1-7, characterized in that: A collection module that collects vibration acceleration signals in typical fault states; A processing module that divides the vibration acceleration signal data into multiple time windows, and uses the sampling data of each time window as the node features of the graph to construct graph structure data; An adjustment module that, based on the graph structure data, uses the structure-aware similarity modeling mechanism to measure the structural similarity between nodes and dynamically adjust the feature aggregation strategy; A calculation module that uses the local adaptive residual feature propagation mechanism to perform multi-layer feature propagation and fusion on the feature aggregation strategy; A classification module that inputs the fused node representation and outputs the corresponding fault type to realize intelligent fault diagnosis.

9. A computer device, comprising: A memory and a processor; the memory stores a computer program, characterized in that: when the processor executes the computer program, the steps of the method according to any one of claims 1-7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by the processor, the steps of the method according to any one of claims 1-7 are implemented.

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