Method and system for identifying critical components of multiple networked industrial software

By calculating the influence radius and multiple eigenvector similarity of components, and combining latent variable models and gravity centrality models, key components in multi-networked industrial software systems are identified, solving the problem of inaccurate identification in existing technologies and improving system stability and production efficiency.

CN119647037BActive Publication Date: 2025-11-28SOUTHEAST UNIV +1
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Patent Information

Application Number
CN202411785231.8
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-12-06
Publication Date
2025-11-28
Estimated Expiration
2044-12-06

AI Technical Summary

Technical Problem

Existing methods for identifying key components in multi-networked industrial software systems neglect the characteristics of different network layers and their impact on the entire system, failing to effectively consider the multiple feature vectors and correlation strength between components, resulting in inaccurate identification.

Method used

One approach is to calculate the influence radius and multiple feature vector similarity of components in each network layer, and combine latent variable model and gravity centrality model to quantify the correlation strength between components and the importance of network layers, construct gravity centrality model, and identify key components.

Benefits of technology

It improves the accuracy and efficiency of identifying key components in multi-networked industrial software systems, enhances the ability to allocate resources and prevent faults in key components, and improves system stability and production efficiency.

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Abstract

The application discloses a kind of key component identification method and system for multiple networked industrial software, first calculate the influence radius of all components on each network layer, calculate the importance degree of each component based on dynamic influence range, then calculate the similarity between multiple feature vectors of each component on different relationship network layer using cosine similarity algorithm, calculate the association strength between different components on different relationship network layer using latent variable model, then calculate the importance LI α Of each network layer G α ;Finally, based on the importance degree of dynamic influence range, the importance LI α Of association strength between different components in network layer G α Construct gravity centrality model, calculate the importance of each component.And according to the importance degree value ranking, thereby identify the key component on multiple networked industrial software system.The method of the application is efficient and reliable, and enhances the identification ability of key components on multiple networked industrial software system.
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Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of intelligent computing, and mainly relates to a key component identification method and system for multiple networked industrial software. BACKGROUND

[0002] Key node identification is one of the most important research problems in network science, and key component identification on a multiple networked industrial software system refers to modeling different components as network nodes in an industrial software component network established on the basis of multiple data flow types associated coupling, and based on the topological connection relationship between components, mining components that have an important influence on the running stability of the multiple networked industrial software system. This result is crucial for exploring the stability of the multiple networked industrial software system. For example, the running error of a few components with greater influence may cause large-scale cascading failures of other components in the multiple networked industrial software system, and even cause the collapse of the entire industrial software system, seriously affecting the efficiency of industrial production. Therefore, an accurate and efficient key component identification method is of great significance for the stable operation of components on the entire industrial software system.

[0003] The core idea of the traditional key component identification method for an industrial software system is to consider the information of the component itself and other related components within its influence range, and calculate the importance of each component by modeling the interaction between them. In addition, the key component identification method is mostly based on the research on single-layer industrial software systems, while the industrial software system at the present stage presents the characteristics of multiple relationships between components, that is, different software components are simultaneously affected by multiple networks of information flow, control flow, business flow and other associated coupling, which correspond to multiple different relationship networks. Abstracting such a complex industrial software system into a single-layer network will ignore the characteristics of different network layers themselves and their influence on the entire industrial software system. Therefore, the simple single-layer network method is no longer suitable for the key component identification research on industrial software systems. In order to effectively and reasonably describe the industrial software with multiple relationships between different components, it is necessary to model the different relationships between components in the industrial software system, and calculate the importance of each component based on the importance of the components under different relationships and the influence of different relationship networks on the entire industrial software system.

[0004] However, the existing research on multiple networks mostly sums up the key component identification results of each layer, without further considering the influence of different network relationships on key component identification. In addition, the existing methods are based on the research on the multiple topology structure of components, ignoring the use of different component multiple feature vectors. For different industrial components, due to the great difference in their application scope, task category, carrying capacity and other aspects, and the same components on different network layers also differ due to different task division and running environment characteristics, therefore different multiple feature vectors should be used to represent the industrial software components on different network layers, but the existing research ignores the use of component characteristics. At the same time, the greater the correlation strength between components, the higher the attraction between them, when calculating the importance of components, not only the properties of the components themselves need to be considered, but also the correlation strength with other components, greater correlation strength reflects higher importance between components, for a specific component, components with higher correlation strength should be given higher weight when calculating importance, but the existing research ignores the modeling of this important phenomenon. SUMMARY

[0005] The present application is directed to the problem of identifying key components in the existing technology of multiple networked industrial software systems, and proposes a key component identification method and system for multiple networked industrial software. First, the influence radius of all components on each network layer is calculated, the importance of each component based on dynamic influence range is calculated Then the cosine similarity algorithm is used to calculate the similarity between the multiple feature vectors of each component on different relationship network layers The association strength between different components on different relationship network layers is calculated using the latent variable model Then the importance LI of each network layer G α is calculated α ; Finally, the importance of each component based on dynamic influence range The association strength between different components The importance LI of network layer G α is calculated α The gravity centrality model is constructed to calculate the importance of each component. According to the importance value, the key components on the multiple networked industrial software system are identified. The method is efficient and reliable, and enhances the identification ability of key components on multiple networked industrial software systems.

[0006] To achieve the above purpose, the technical scheme adopted by the present application is: a key component identification method for multiple networked industrial software, comprising the following steps:

[0007] S1: input components into a multi-networked industrial software system G = {G1, G2, …, G L} containing L different relationships, each layer of the multi-networked industrial software system contains N identical components;

[0008] S2: calculate the influence radius of all components on each network layer, and determine the component influence together with the average influence radius of its neighbor components, and calculate the importance degree of each component based on dynamic influence range

[0009] S3: calculate the similarity between the multi-feature vectors of each component on different relationship network layers, and calculate the similarity by using cosine similarity algorithm obtained;

[0010] S4: calculate the correlation strength between different components on different relationship network layers using latent variable model The correlation strength is determined based on the similarity of step S3

[0011] S5: calculate the importance of each network layer G α , the importance LI α of the network layer is obtained by comparing the ratio of the number of edges in the network layer to the total number of edges in the multi-network

[0012] S6: according to the importance degree of the component based on dynamic influence range obtained in step S2 , the correlation strength between different components obtained in step S4 , and the importance LI α of the network layer G α obtained in step S5, construct the gravity centrality model as follows:

[0013]

[0014] wherein, represents the shortest path length of the component and on the network layer ;

[0015] The importance degree of each component is as follows:

[0016]

[0017] S7: sort the importance degree value of each component obtained in step S6, thereby identifying the key components on the multi-networked industrial software system.

[0018] As an improvement of the present invention, in step S1, the network layer G of the multi-networked industrial software system α Components on and The multiple topological structures between them are represented as follows:

[0019]

[0020] in, Represents network layer G α The i-th component on, Representation Component and At network layer G α There is a connection above.

[0021] As an improvement of the present invention, step S2 specifically includes the following steps:

[0022] S21: Introduce the iterative k-shell algorithm and gravity centrality model, and define nodes. For any other node The applied gravitational center of gravity is:

[0023]

[0024]

[0025] in, Representing nodes respectively and The degree, express and The shortest distance between, Indicates the gravity coefficient. Represents a node Iterative k-shell values, Iks max Iks min These represent network layers G respectively. α The maximum and minimum iterative k-shell values ​​of the nodes;

[0026] For nodes and The dividing point Define nodes respectively and For nodes Applied gravitational centrality:

[0027]

[0028]

[0029] S22: According to the force balance principle, the nodes and The gravity applied to the node is equal, then:

[0030]

[0031] S23: Using the above equation to solve , the influence radius of the node is obtained The solving formula of the influence radius of the node

[0032]

[0033] S24: Calculate the importance degree based on the dynamic influence range of each component

[0034]

[0035] Wherein, The number of neighbors of the component .

[0036] In order to achieve the above purpose, the technical scheme adopted by the present application is: for the key component identification system of multi-networked industrial software, at least including component influence range calculation module, correlation strength calculation module, network layer importance calculation module and component importance comprehensive evaluation module;

[0037] The component influence range calculation module: based on the topological connection between components on the whole multi-networked industrial software system, the influence range of each component is calculated, and the importance degree of each component based on the dynamic influence range is obtained;

[0038] The correlation strength calculation module: the multi-feature vector and the multi-topological structure of the component are combined, and the correlation strength of different relationship network layers between components is solved by constructing a hidden variable model;

[0039] The network layer importance calculation module: by considering the influence of different relationship networks on the network structure of the whole industrial software system, the importance degree of each different relationship network to the whole industrial software system is calculated;

[0040] The component importance comprehensive evaluation module: by constructing a gravity centrality model based on weight, combining the calculated correlation strength, component centrality based on influence range and network layer importance, the overall importance degree of each component is obtained, so as to identify the key components on the multi-networked industrial software system.

[0041] Compared with the prior art, the present application has the beneficial effects:​

[0042] (1) The method of the present application combines the multiple feature vectors and the multiple topological structures of each component on the multiple networked industrial software system for the first time, and infers the correlation strength between different components on the multiple networked industrial software system by constructing a latent variable model.

[0043] (2) The present application models the relationship types between industrial software components in a multiple networked environment, and quantifies the influence degree of different relationship types on the importance of industrial software components. The influence of different relationship networks on the overall structure of the multiple networked industrial software system is considered in the process of identifying key components, and the importance of each different relationship network to the multiple networked industrial software system is calculated, enhancing the ability to distinguish different network layers in the component relationship network.

[0044] (3) The present application constructs an improved weighted gravity model, which can more accurately reflect the attraction degree between components based on the correlation strength, and combines the correlation strength between industrial software components and the importance of different relationship types to obtain a sequence of components that have important influence on the entire multiple networked industrial software system, enhancing the ability to identify key components on the multiple networked industrial software system.

[0045] (4) The present application uses the multiple feature vectors and the multiple topological structures of the components to identify key components on the multiple networked industrial software system. The addition of multiple feature vectors makes the information considered in identifying key components more comprehensive, not only considering the structural information of the entire multiple industrial software network, but also considering the characteristics of different components themselves, further improving the effect of key component identification. BRIEF DESCRIPTION OF DRAWINGS

[0046] Figure 1 is the overall framework diagram of the method of the present application;

[0047] Figure 2 is the connection diagram between components on the multiple networked industrial software system in embodiment 2 of the present application. DETAILED DESCRIPTION

[0048] The present application will be further illustrated below in conjunction with the drawings and specific embodiments, and it should be understood that the following specific embodiments are only used to illustrate the present application and not to limit the scope of the present application.

[0049] Embodiment 1

[0050] For the key component identification method of multiple networked industrial software system, the existing method is based on the multiple topology structure of the component, ignores the actual situation of different components in the multiple industrial software network, and does not further consider the influence of different network relations on the key component identification, and there is almost no more research on the correlation strength which can accurately reflect the attraction degree between components, so the application discloses a kind of key component identification method suitable for multiple networked industrial software system, as shown in Figure 1 The specific implementation process is as follows:

[0051] Step S1: input the multiple networked industrial software system G containing L different relations G={G1, G2, …, G L Each layer network contains N identical components, for multiple networked industrial software system G, The i (1≤i≤N) component on network layer G α (1≤α≤L) is represented as C α The multiple topology structure between the components And On network layer G α Can be represented as:

[0052]

[0053] Wherein, Indicate that components And There is a connection on network layer G α

[0054] Step S2: calculate the influence radius of all components on each network layer.

[0055] The method considers the difference of the influence range of different components, obtains different influence radius for each component on multiple networked industrial software system, so as to accurately describe the heterogeneous characteristics of components in complex network. Specifically, for component Its influence range is represented as This means that component In network layer G α Can influence up to its Level neighbor. It is assumed that for any component There is a component Outside the influence range in the same layer relationship network, and components And Have overlapping influence range. In the overlapping range, there is a component Not only the Level neighbor of component But also the Level neighbor of component level neighbors. Obviously, component is located on the shortest path between component and In this sense, component can be regarded as the demarcation point between component and .

[0056] Step S21: Introduce the iterative k-shell algorithm and the gravity centrality model, define the gravity centrality of node on other arbitrary nodes :

[0057]

[0058]

[0059] wherein, denote the degrees of node and , respectively, denote the shortest distance between and , and denote the gravity coefficient, which is used to describe the degree of mutual attraction between nodes, denote the iterative k-shell value of node , Iks max , Iks min denote the maximum and minimum iterative k-shell values of nodes in network layer G α , respectively.

[0060] The demarcation point between node and is defined as the gravity centrality of node and on node :

[0061]

[0062]

[0063] Step S22: According to the principle of force balance, the gravity exerted by node and on node is equal, then:

[0064]

[0065] Step S23: Solve the above equation for , and obtain node the influence radius of the component The solution formula is:

[0066]

[0067] Step S24: The influence of the component defined by the method of the present application is determined by the influence radius of the component itself and the average influence radius of its neighbor components. Therefore, after obtaining the corresponding influence radius of each component , the method of the present application calculates the importance degree of each component based on the dynamic influence range

[0068]

[0069] wherein, n represents the number of elements contained in the multiple feature vectors used. represents the number of neighbors of the component .

[0070] Step S3: Calculate the similarity between the multiple feature vectors of each component in different relationship network layers.

[0071] The multiple feature vectors of the component defined by the method of the present application can be represented as: wherein C i1 , C i2 , …, C in are different feature representations of the component . Based on the vectors, the cosine similarity algorithm is used to calculate the similarity between the multiple feature vectors of different components and in the network layer G α :

[0072]

[0073] wherein, n represents the number of elements contained in the multiple feature vectors used.

[0074] Step S4: Use the latent variable model to calculate the association strength between different components in different relationship network layers.

[0075] The latent variable model is based on two observations: (1) for two components and , given a specific relationship network layer G α , the association strength is determined by the similarity between the multiple feature vectors of the components and in the network layer G α .(2) and in the relationship network layer Gα the strength of the association on the relation network layer G influences their multiple topologies on G α

[0076] The latent variable model represents the possible causal relationships between all variables by modeling conditional dependencies. Based on these dependencies, the joint distribution factorizes as follows:

[0077]

[0078] where represents and the strength of the association on the relation network layer G α

[0079] The method of the invention employs widely used Gaussian distributions to model the conditional probabilities and as follows:

[0080]

[0081] where w α is the weight to be estimated and v is the variance in the Gaussian model. In the same way, the dependencies between and are modeled as follows:

[0082]

[0083] where β α is the parameter to be learned. Given and the similarity of the multiple feature vectors on the relation network layer C α the multiple topologies between components the strength of the association The joint probability can be expressed as:

[0084]

[0085] where λ1and λ2are preset parameters, is the set of pairs of components on the network layer G α

[0086] Since the above joint probability is independent, the method of the invention can factorize it into L independent joint probabilities and derive the solution for each relation network layer. Thus, it is only necessary to derive the solution for the joint probability of the a-th relation network layer. Take the logarithm of the above equation and list only the log-likelihood of the a-th relation network layer: ​​​​

[0087]

[0088] Since the function is a concave function, the method uses a gradient-based strategy to optimize the parameters, the coordinate ascent optimization method iteratively updates w α , β α , until convergence. For different parameters, the gradient in the coordinate direction is respectively:

[0089]

[0090]

[0091]

[0092] In each iteration, the method uses the Newton-Raphson method to update the above parameters:

[0093]

[0094]

[0095]

[0096] Where the second derivative of each parameter is given by:

[0097]

[0098]

[0099]

[0100] After convergence, the final is the association strength of components and on the component relationship network layer G α of the multi-network industrial software system.

[0101] Similarly, the method can obtain the association strength between components on different network layers.

[0102] Step S5: Calculate the importance of each network layer G α .

[0103] The importance of the network layer G α in the multi-layer network is represented as LI α , which is calculated by comparing the number of edges in the network layer with the total number of edges in the multi-network. The ratio can be given by:

[0104]

[0105] in It is the network layer G α The number of sides, It represents the total number of edges in the entire multi-element network.

[0106] LI α It can quantify the contribution of each network layer to the overall multi-layer network structure. Layers with high importance indicate that they play a crucial role in the multi-layer network, while layers with low importance contribute less to the overall network structure.

[0107] Step S6: Construct a weighted gravity centrality model.

[0108] As described above, the components were obtained. Importance based on the dynamic scope of influence Correlation strength between different components Network layer G α Importance LI α Based on the above results, the gravity centrality model is constructed as follows:

[0109]

[0110] in, Representation Component and In the network layer The shortest path length on the network layer, if there is no direct path between two components on that network layer, then The value is negative infinity.

[0111] Based on the above results, the importance of each component is as follows:

[0112]

[0113] Step S7: Sort the components according to their importance values ​​to identify key components in the multi-networked industrial software system, provide guidance for collaboration and decision-making among components, and improve the overall production and operation efficiency of the industrial software.

[0114] Example 2

[0115] This patent's new technology addresses the processing of multiple networked industrial software components. Because these components can be independently developed, deployed, run, upgraded, and interconnected, they achieve adaptive switching of service composition modes and dynamic adjustment of service granularity, forming multi-granularity component services. In real-world scenarios of multiple networked industrial software systems, industrial components are influenced by multiple interconnected coupling methods, including data flow, business flow, and information flow. For example, the component connections in a simple multiple networked industrial software system might look like this: Figure 2 As shown, different layers G1 to G1 represent different coupling relationships experienced by the component. In different associated coupling layers G... α In China, industrial software components Based on the actual business processes of industrial software systems and their connection with other components, this paper proposes a key component identification system for multi-networked industrial software systems based on association strength. This system implements the method described in Example 1. The system addresses the issues of green efficiency improvement, flexible service, and intelligent deployment of industrial software components, providing strong technical support for enhancing the efficiency, robustness, and scalability of industrial software systems in multi-network environments. The system includes at least four different functional modules: a component influence range calculation module, an association strength calculation module, a network layer importance calculation module, and a comprehensive component importance evaluation module.

[0116] The component influence range calculation module calculates different influence radii for each component in the multi-networked industrial software system based on the different influence ranges of different components, and obtains the importance of each component based on the dynamic influence range. The association strength calculation module combines the multiple feature vectors and multiple topologies of the components, and solves the association strength of different relationship network layers between components by constructing a latent variable model. The network layer importance calculation module calculates the importance of each relationship network to the entire multi-networked industrial software system by considering the impact of different relationship networks on the overall structure of the multi-networked industrial software system. The component importance comprehensive evaluation module constructs a weighted gravity centrality model, combines the calculated association strength, component centrality based on influence range, and network layer importance to obtain the overall importance of each component, thereby identifying the key components in the multi-networked industrial software system.

[0117] In summary, the method of the present application is based on the correlation strength gravity centrality method combining intrinsic and topological features (ITFRSGC), and a key component identification method and system based on correlation strength in a multi-networked industrial software system are proposed. The method simultaneously uses multiple feature vectors and multiple topological structures of components for key component identification for the first time, and models the correlation strength between different components in different relationship networks based on the above information. The importance of different relationship networks for key component identification is considered, and the key components in the multi-networked industrial software system are more efficiently identified. For example, the relatively more critical components are emphasized for monitoring, more resources are allocated to these components, and the phenomenon of large-scale cascading failures of other components in the multi-networked industrial software system caused by the failure of these components is prevented. Guidance is provided for component cooperation and decision-making, and the overall production and operation efficiency is improved.

[0118] It should be noted that the above content only illustrates the technical idea of the present application, and cannot be used to limit the protection scope of the present application. For ordinary skilled persons in the art, several improvements and refinements can be made without departing from the principles of the present application, and these improvements and refinements fall within the protection scope of the claims of the present application.

Claims

1. A method for identifying key components of multi-networked industrial software, characterized in that, Includes the following steps: S1: Input the component into a multi-layered networked industrial software system G = {G1, G2, ..., G...} containing L different relationships. L In the aforementioned multi-networked industrial software system, each network layer contains N identical components; S2: Calculate the influence radius of all components in each network layer, and combine it with the average influence radius of its neighboring components to determine the influence of each component. Calculate the importance of each component based on its dynamic influence range. S3: Calculate the similarity between the multiple feature vectors of each component at different relational network layers. The similarity is calculated using a cosine similarity algorithm. get; S4: Use latent variable models to calculate the association strength between different components at different layers of the relational network. The correlation strength Based on the similarity in step S3 Sure; S5: Calculate G for each network layer α The degree of importance, the importance LI α This is determined by comparing the ratio of the number of edges in this network layer to the total number of edges in the multi-layer network; S6: Components obtained from step S2 Importance based on the dynamic scope of influence The correlation strength between different components obtained in step S4 The network layer G obtained in step S5 α Importance LI α The gravity centerity model is constructed as follows: in, Representation Component and In the network layer The shortest path length on; The importance of each component is as follows: S7: Sort the importance values ​​of each component obtained in step S6 to identify the key components in the multi-networked industrial software system.

2. The method for identifying key components of multi-networked industrial software as described in claim 1, characterized in that: In step S1, the network layer G of the multi-networked industrial software system... α Components on and The multiple topological structures between them are represented as follows: in, Represents network layer G α The i-th component on, Representation Component and At network layer G α There is a connection above.

3. The method for identifying key components of multi-networked industrial software as described in claim 2, characterized in that: Step S2 specifically includes the following steps: S21: Introduce the iterative k-shell algorithm and gravity centrality model, and define nodes. For any other node The applied gravitational center of gravity is: in, Representing nodes respectively and The degree, express and The shortest distance between, Indicates the gravity coefficient. Represents a node Iterative k-shell values, Iks max Iks min These represent network layers G respectively. α The maximum and minimum iterative k-shell values ​​of the nodes; For nodes and The dividing point Define nodes respectively and For nodes Applied gravitational centrality: S22: According to the principle of force balance, node and For nodes If the applied gravitational forces are equal, then: S23: Use the equation from step S22 to... Solve the problem to obtain the nodes. radius of influence The solution formula is as follows: S24: For each component Calculate the importance based on the dynamic range of influence. in, Representation Component The number of neighbors.

4. The method for identifying key components of multi-networked industrial software as described in claim 1, characterized in that: In step S3, the component The multiple eigenvectors are represented as follows: Where C i1 C i2 ,…,C in It is a component Different feature representations, different components and At network layer G α The similarity between multiple feature vectors is specifically as follows: Where n represents the number of elements contained in the multiple feature vector used.

5. The method for identifying key components of multi-networked industrial software as described in claim 4, characterized in that: Step S4 specifically includes the following steps: S41: The latent variable model models conditional dependencies, and based on these dependencies, the joint distribution decomposes as follows: in, express and At the relational network layer G α The strength of the correlation on; S42: Use a Gaussian distribution to simulate conditional probability. and The dependencies between them are as follows: Among them, w α Let v be the weight to be estimated, and v be the variance in the Gaussian model. and The dependencies between them are modeled as follows: Where β α These are the parameters to be learned. S43: Given and At the relational network layer G α Similarity of multiple feature vectors Multiple topologies between components Correlation strength The joint probability can be expressed as: Where λ1 and λ2 are preset parameters. For network layer G α The set consisting of the components above; S44: Decompose the joint probability from step S43 into L independent joint probabilities, and derive the solution for each relational network layer. Only the solution for the joint probability of the α-th relational network layer needs to be derived. Take the logarithm of the above formula and list only the log-likelihood of the α-th relational network layer: Due to the function It is a concave function; S45: Using a gradient-based strategy to optimize parameters, the coordinate ascent optimization method iteratively updates w. α β α , Until convergence, the gradients in the coordinate directions for different parameters are as follows: In each iteration, the Newton-Raphson method is used to update the above parameters: The second derivatives of each parameter are derived from the following equation: S46: After convergence, the final... For components and In the component relationship network layer G of a multi-networked industrial software system α The strength of the correlation.

6. The method for identifying key components of multi-networked industrial software as described in claim 1, characterized in that: The importance of each network layer in step S5 is determined by LI. α The specific calculation method is as follows: in It is the network layer G α The number of sides, It represents the total number of edges in the entire multi-element network.

7. A key component identification system for multi-networked industrial software using the method described in claim 1, characterized in that: It should include at least a module for calculating the scope of component influence, a module for calculating the correlation strength, a module for calculating the importance of network layers, and a module for comprehensively evaluating the importance of components. The component influence range calculation module calculates the influence range of each component based on the topological connection between components in the entire multi-networked industrial software system, and obtains the importance of each component based on the dynamic influence range. The association strength calculation module combines the multiple feature vectors and multiple topological structures of the components, and solves the association strength of different relationship network layers between the components by constructing a latent variable model. The network layer importance calculation module: by considering the impact of different relational networks on the overall network structure of the industrial software system, calculates the importance of the network layer to the entire industrial software system for each different relational network; The component importance comprehensive evaluation module: by constructing a weighted gravity centrality model, and combining the calculated correlation strength, component centrality based on influence range, and network layer importance, the overall importance of each component is obtained, thereby identifying key components in a multi-networked industrial software system.

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