A complex product module division method based on multi-component correlation analysis

Abstract

The application discloses a kind of based on the complex product module division method of multiple component correlation analysis.The steps of the present application are as follows: first, the final comprehensive correlation strength matrix of component is established from the perspective of product life cycle;Then, through the core component screening method based on the point weight ordering of undirected weighted network, multiple core components are screened out;Then, through the stable overlapping community discovery algorithm based on the shapley value determination in community, the complex product module division is realized, and multiple module division preliminary schemes are generated;If there are overlapping components between each module in the scheme, then assign these overlapping components to the most suitable module through genetic algorithm, and determine the final module division scheme by comparing the modularization measurement value Q of each module division candidate scheme.The present application is suitable for the module division of complex product with a large number of components, and can quickly generate the final scheme of complex product module division.

Description

Technical Field

[0001] This invention relates to a product module partitioning method, and more particularly to a complex product module partitioning method based on multi-component correlation analysis. Background Technology

[0002] Modular product design, as an advanced design methodology, improves product design efficiency, shortens product development cycles, reduces production costs, enables personalized product customization and rapid development of new products, and adapts to rapidly changing market demands. It is a key technology and important implementation method for mass product customization. Product module division is the foundation and essential content of modular design, and the rationality of module division is a crucial factor determining the success of modular design. On the one hand, product module division can shorten product development and manufacturing cycles to meet the needs of mass customization, enabling rapid response to market changes. On the other hand, product module division facilitates the rapid assembly and disassembly of large mechanical equipment, simplifying maintenance. Furthermore, product module division accelerates the processing and recycling of waste products.

[0003] In recent years, scholars have conducted extensive and in-depth research on product module partitioning methods, which can be broadly categorized into optimization algorithms and clustering algorithms. Optimization algorithms, including genetic algorithms, particle swarm optimization, and cuckoo search algorithms, are commonly used for product module partitioning. However, for complex products with a large number of parts, optimization algorithms are inefficient, prone to getting trapped in local optima, and the resulting module partitioning may not be the optimal solution. Among clustering algorithms, graph-based clustering is representative, including Markov clustering and the improved Girvan-Newman (GN) algorithm. Markov clustering is not suitable for large graphs, so it may not be able to generate module partitioning results for complex products, making it unsuitable for complex product module partitioning. Although the improved GN algorithm can generate module partitioning results for complex products, it is not necessarily the optimal solution and is time-consuming.

[0004] Existing product module partitioning methods are mainly applied to simple products with a small number of parts, while methods applicable to complex products with a large number of parts are rare. Therefore, it is essential to propose a method suitable for module partitioning of complex products. Summary of the Invention

[0005] To address the problems existing in the background technology, this invention proposes a method for dividing complex product modules based on multi-component correlation analysis.

[0006] The technical solution adopted in this invention includes the following steps:

[0007] Step 1: Establish the final comprehensive correlation strength matrix of components from the perspective of the entire product life cycle;

[0008] Step 2: Based on the final comprehensive correlation strength matrix of components, use the core component screening method based on undirected weighted network point weight sorting to obtain multiple core components and obtain the initial core node set;

[0009] Step 3: Based on the initial core node set, use the stable overlapping community detection algorithm based on the Shapley value determination within the community to divide the complex product into modules and obtain multiple preliminary module division schemes;

[0010] Step 4: Optimize and select multiple preliminary module partitioning schemes using a genetic algorithm-based overlapping component allocation method to obtain the final module partitioning scheme.

[0011] In step 1, the final comprehensive correlation strength matrix C of the components is a correlation strength sub-matrix C based on customer requirements. N Functional correlation strength submatrix C F Structural correlation strength submatrix C S Material category correlation strength submatrix C M Process correlation strength submatrix C T , Maintaining the frequency correlation strength submatrix C P Lifetime correlation strength submatrix C L The correlation strength submatrix C with the recycling method R Obtained through calculation.

[0012] Step 1 specifically involves:

[0013] First, the customer demand correlation strength submatrix C N Functional correlation strength submatrix C F Structural correlation strength submatrix C S Material category correlation strength submatrix C M Process correlation strength submatrix C T , Maintaining the frequency correlation strength submatrix C P Lifetime correlation strength submatrix C L The correlation strength submatrix C with the recycling method R After weighted summation, the component comprehensive correlation strength matrix C1 in fuzzy number form is obtained, and the calculation formula is as follows:

[0014] C1(i,j)=S1C N (i,j)+S2C F (i,j)+S3C S (i,j)+S4C M (i,j)+S5C T (i,j)+

[0015] S6C P(i,j)+S7C L (i,j)+S8C R (i,j)

[0016] Where S1-S8 are the first to eighth weight coefficients, respectively, 1≤i≤n, 1≤j≤n, n is the total number of parts in the complex product, and C N (i,j) represents the customer demand correlation strength between the i-th component and the j-th component, C F (i,j) represents the functional association strength between the i-th component and the j-th component, C S (i,j) represents the structural correlation strength between the i-th component and the j-th component, C M (i,j) represents the material category association strength between the i-th component and the j-th component, C T (i,j) represents the process correlation strength between the i-th component and the j-th component, C P (i,j) represents the maintenance frequency correlation strength between the i-th component and the j-th component, C L (i,j) represents the service life correlation strength between the i-th component and the j-th component, C R (i,j) represents the correlation strength of the recycling methods between the i-th component and the j-th component;

[0017] Next, the component comprehensive correlation strength matrix C1 in fuzzy number form is converted into the component comprehensive correlation strength matrix C2 in real number form. After standardizing the component comprehensive correlation strength matrix C2 in real number form, the final comprehensive correlation strength matrix C is obtained.

[0018] Step 2 specifically involves:

[0019] First, we introduce complex network theory and construct a real undirected weighted network G based on the final comprehensive correlation strength matrix C of the components, as shown in the following formula:

[0020] G = (V, E, W)

[0021] Where V represents the set of nodes in the real undirected weighted network G, where each node represents a component of the product; E represents the set of edges in the real undirected weighted network G, where each edge represents the relationship between two components; and W represents the set of edge weights in the real undirected weighted network G, where each edge weight represents the final comprehensive relationship strength between two components.

[0022] Next, the transition matrix J is established based on the edge weight set of the real undirected weighted network G, as shown in the following formula:

[0023]

[0024] Where J(i,j) represents the transition coefficient between the i-th component and the j-th component, C(i,j) represents the final comprehensive correlation strength between the i-th component and the j-th component, and α represents the correlation strength threshold;

[0025] Next, calculate the node weights corresponding to all components of the complex product, using the following formula:

[0026]

[0027] Among them, v r ω represents the node weight corresponding to component r. rz The weight of the z-th edge connected to the node corresponding to component r is given by g, and the total number of edges connected to the node corresponding to component r is given by g.

[0028] Finally, based on the transition matrix J and the point weights of all nodes, the core nodes corresponding to multiple core components are selected according to the Pareto principle, thereby obtaining the initial core node set.

[0029] The process involves using the transition matrix J and the point weights of all nodes to select core nodes corresponding to multiple core components according to the Pareto principle, specifically as follows:

[0030] Several nodes are selected as core nodes in descending order of their point weights, and the transition coefficient J(i,j) between any two core nodes and their corresponding core components is 0.

[0031] Step 3 specifically involves:

[0032] Step 3.1: Set the initial stability coefficient ε;

[0033] Step 3.2: Create a new empty community, denoted as B, where the community represents a module of the product; place the core node with the highest node weight in the current core node set into community B;

[0034] Step 3.3: In a real undirected weighted network G, if the maximum edge weight C connecting the inside and outside of community B is... max If the number of nodes is greater than or equal to the expansion threshold δ, then community B can continue to expand, and proceed to step 3.4; otherwise, no more nodes can be added to community B to form a complete community, and proceed to step 3.11.

[0035] Step 3.4: In a real undirected weighted network G, find a node outside community B such that the edge weight between this node and a node inside community B is equal to the maximum edge weight C connecting the inside and outside of community B. max Place the node in community B;

[0036] Step 3.5: Let the auxiliary undirected weighted network G1 be the real undirected weighted network G. At this time, the number of nodes in the current community B is set to n1.

[0037] Step 3.6: Within community B, calculate the maximum Shapley value and the Shapley value of each node in community B based on the real undirected weighted network G. According to the current stability coefficient ε and the maximum and Shapley values ​​of each node in community B, sequentially determine whether each node in community B satisfies the following inequality. If a node satisfies the following inequality, then that node affects the stability of community B, and proceed directly to step 3.7; if none of the nodes in community B satisfy the following inequality, then community B is stable, and proceed to step 3.8. The formula is as follows:

[0038]

[0039]

[0040] in, This represents the Shapley value of node i in community B. Let represent the maximum Shapley value of node i, β represent the proportion of the sum of the final comprehensive association strengths, C(i,j) represent the final comprehensive association strength between the i-th component and the j-th component, and V represent the node set of the real undirected weighted network G;

[0041] Step 3.7: Delete the node within community B that affects the stability of community B, move the node from inside community B to outside community B, and delete the edge connecting the node to other nodes within community B from the auxiliary undirected weighted network G1. Proceed to step 3.6.

[0042] Step 3.8: If the actual number of nodes in community B is n1 at this time, go to step 3.3; otherwise, go to step 3.9.

[0043] Step 3.9: In the auxiliary undirected weighted network G1, if the maximum edge weight C connecting the inside and outside of community B is... max If the value is greater than or equal to the expansion threshold δ, then community B can continue to expand, proceed to step 3.10; otherwise, no more nodes can be added to community B to form a complete community, proceed to step 3.11.

[0044] Step 3.10: In the auxiliary undirected weighted network G1, find a node outside community B such that the edge weight between this node and a node inside community B is equal to the maximum edge weight C connecting the inside and outside of community B. max Place the node in community B and proceed to step 3.6;

[0045] Step 3.11: Remove the core nodes that have been added to Community B from the core node set;

[0046] Step 3.12: Determine if the current core node set is empty; if the core node set is not empty, proceed to step 3.2; if the core node set is empty, multiple communities have been formed, proceed to step 3.13.

[0047] Step 3.13: Generate a preliminary module division plan based on the existing multiple communities;

[0048] Step 3.14: Change the value of the stability coefficient ε and repeat steps 3.2-3.13 to obtain preliminary module partitioning schemes corresponding to different stability coefficients ε, thereby obtaining multiple preliminary module partitioning schemes.

[0049] Step 4 specifically involves:

[0050] Step 4.1: Divide the preliminary schemes into multiple modules to form an initial first scheme set;

[0051] Step 4.2: Select any solution from the current first solution set and delete that solution from the first solution set;

[0052] Step 4.3: Determine whether there are overlapping parts between the modules in the current solution; if there are overlapping parts between the modules, proceed to step 4.4; if there are no overlapping parts between the modules, proceed to step 4.6.

[0053] Step 4.4: Filter out overlapping components in the current solution and delete these components from each module of the current solution;

[0054] Step 4.5: Use the current number of overlapping parts as the chromosome length L in the genetic algorithm, and use the genetic algorithm to assign these overlapping parts to the most suitable modules to obtain a new module partitioning scheme;

[0055] Step 4.6: Add the current solution to the second solution set as a candidate solution for module partitioning;

[0056] Step 4.7: Determine if there are any remaining solutions in the first solution set; if there are remaining solutions, proceed to step 4.2; if there are no remaining solutions, proceed to step 4.8.

[0057] Step 4.8: By comparing the modularity metric Q of each module partitioning candidate scheme in the second scheme set, the module partitioning candidate scheme with the largest modularity metric Q is taken as the final module partitioning scheme.

[0058] The beneficial effects of this invention are:

[0059] 1) A stable overlapping community detection algorithm based on Shapley value determination within the community and an overlapping component allocation method based on genetic algorithm are proposed. These methods are suitable for module partitioning of complex products with a large number of components and solve the problem that many existing methods may not be able to achieve good module partitioning of complex products with a large number of components.

[0060] 2) The proposed stable overlapping community detection algorithm based on Shapley value determination within the community can quickly and effectively obtain a preliminary scheme for the partitioning of complex product modules. Regarding the proposed overlapping component allocation method based on genetic algorithm, because the chromosome length equals the number of overlapping components, and the chromosome length is relatively short, there is no need to set a large population size and a termination generation number, thus enabling the rapid allocation of overlapping components to the most suitable modules.

[0061] 3) A comprehensive correlation strength matrix for components is established from the perspective of the entire product lifecycle, focusing not only on the design and manufacturing stages but also on the maintenance, scrapping, and recycling stages, thus improving the maintainability and recyclability of the product. A core component screening method based on undirected weighted network point weight ranking is proposed, which can screen out representative core components and save program execution time for subsequent module partitioning. Attached Figure Description

[0062] Figure 1 This is a schematic diagram of the overall process of the method of the present invention.

[0063] Figure 2 This is a component comprehensive correlation strength decomposition model based on multi-source related information.

[0064] Figure 3 This is a flowchart illustrating the algorithm for detecting stable overlapping communities based on Shapley values ​​within the community.

[0065] Figure 4 This is a flowchart illustrating the process of assigning overlapping components based on a genetic algorithm.

[0066] Figure 5 Examples of chromosome encoding, chromosome crossing over, and chromosome variation operations.

[0067] Figure 6 This is a schematic diagram of the population variation process. Detailed Implementation

[0068] To achieve the modular division of complex products, this invention verifies the above-mentioned modular division method using a certain model of CNC grinding machine as an example. The overall flowchart of the method involved is shown below. Figure 1 As shown, the specific implementation steps are as follows:

[0069] Step 1: As Figure 2As shown, a component comprehensive correlation strength decomposition model based on multi-source related information is constructed from the perspective of the entire product life cycle, and the final comprehensive correlation strength matrix of components is established based on the component comprehensive correlation strength decomposition model;

[0070] In step 1, the final comprehensive correlation strength matrix C of the components is a correlation strength submatrix C based on customer requirements. N Functional correlation strength submatrix C F Structural correlation strength submatrix C S Material category correlation strength submatrix C M Process correlation strength submatrix C T , Maintaining the frequency correlation strength submatrix C P Lifetime correlation strength submatrix C L The correlation strength submatrix C with the recycling method R Obtained through calculation.

[0071] First, the customer demand correlation strength submatrix C N Functional correlation strength submatrix C F Structural correlation strength submatrix C S Material category correlation strength submatrix C M Process correlation strength submatrix C T , Maintaining the frequency correlation strength submatrix C P Lifetime correlation strength submatrix C L The correlation strength submatrix C with the recycling method R After weighted summation, the component comprehensive correlation strength matrix C1 in fuzzy number form is obtained, and the calculation formula is as follows:

[0072] C1(i,j)=S1C N (i,j)+S2C F (i,j)+S3C S (i,j)+S4C M (i,j)+S5C T (i,j)+S6C P (i,j)+S7C L (i,j)+S8C R (i,j)

[0073] Where S1-S8 are the first to eighth weighting coefficients, respectively, 1≤i≤n, 1≤j≤n, and n is the total number of parts in the complex product. In this embodiment, the CNC grinding machine has 133 parts, i.e., n=133. N (i,j) represents the customer demand correlation strength between the i-th component and the j-th component, C F (i,j) represents the functional association strength between the i-th component and the j-th component, CS (i,j) represents the structural correlation strength between the i-th component and the j-th component, C M (i,j) represents the material category association strength between the i-th component and the j-th component, C T (i,j) represents the process correlation strength between the i-th component and the j-th component, C P (i,j) represents the maintenance frequency correlation strength between the i-th component and the j-th component, C L (i,j) represents the service life correlation strength between the i-th component and the j-th component, C R (i,j) represents the correlation strength between the recycling methods of the i-th component and the j-th component.

[0074] In practice, the numerical value of the association strength in each submatrix is ​​represented by a trapezoidal fuzzy number, and its membership function is... The formula is as follows:

[0075]

[0076] Where a≤b≤c≤d, a, b, c, and d represent the first to fourth groups of the trapezoidal fuzzy number, respectively.

[0077] Let A r Represents the trapezoidal fuzzy number A f =The real number corresponding to (a,b,c,d); the trapezoidal fuzzy number can be converted into a real number using the following formula:

[0078] A r = (a+b+c+d) / 4

[0079] Next, the component comprehensive correlation strength matrix C1 in trapezoidal fuzzy number form is converted into the component comprehensive correlation strength matrix C2 in real number form using the above formula. After standardizing the component comprehensive correlation strength matrix C2 in real number form, the final comprehensive correlation strength matrix C is obtained. The standardization formula is as follows:

[0080]

[0081] Where C(i,j) represents the final comprehensive association strength between the i-th component and the j-th component; C2(i,j) represents the real number corresponding to the comprehensive association strength between the i-th component and the j-th component, which is obtained by converting the comprehensive association strength of the components represented by trapezoidal fuzzy numbers into real numbers.

[0082] In this embodiment, a certain model of CNC grinding machine is taken as an example. The main components of the CNC grinding machine are shown in Table 1.

[0083] Table 1 shows the main components of a CNC grinding machine.

[0084]

[0085]

[0086]

[0087]

[0088] Regarding the strength of customer demand correlation, in the design process of complex products, due to their personalized and customized characteristics, customers typically interact with designers to meet their needs, making the importance of customer needs self-evident. During the modularization of complex products, related components should be integrated into the same module as much as possible according to customer needs and preferences to improve customer satisfaction. The assessment of the strength of customer demand correlation between components is shown in Table 2, C. N (i,j) represents the strength of customer demand correlation between the i-th component and the j-th component.

[0089] Table 2 shows the correlation strength between customer demand for different components.

[0090]

[0091]

[0092] Regarding the strength of functional association, a certain function of a complex product may be implemented by one or more components. During the module partitioning process of a complex product, the strength of functional association is assessed based on whether two components can jointly implement the same sub-function and whether they can jointly implement the same main function. Components that jointly implement the same function should be grouped into the same module whenever possible. The assessment of the strength of functional association between components is shown in Table 3, C. F (i,j) represents the functional association strength between the i-th component and the j-th component.

[0093] Table 3 shows the functional correlation strength between components.

[0094]

[0095] Regarding structural correlation strength, it depends on the connection method between two components. The connection method determines the ease of disassembly between the components; the more difficult it is to disassemble the two components, the stronger their structural correlation strength. In the process of dividing complex product modules, components that are difficult to disassemble should be grouped into the same module as much as possible. The assessment of the structural correlation strength between components is shown in Table 4, C. S (i,j) represents the structural correlation strength between the i-th component and the j-th component.

[0096] Table 4 shows the structural correlation strength between components.

[0097]

[0098]

[0099] Regarding the material category correlation strength, if a module contains components made of different materials, more effort is required to recycle that module. During the modularization of complex products, components with the same material category should be grouped into the same module as much as possible. This helps improve manufacturing and recycling efficiency and reduces recycling costs. The material category correlation strength assessment between components is shown in Table 5, C. M (i,j) represents the material category association strength between the i-th component and the j-th component.

[0100] Table 5 shows the correlation strength between material categories of components.

[0101]

[0102] Regarding the strength of process correlation, each component has its own process. If the processes of components are the same or similar, it is possible that components from the same module will be processed simultaneously during manufacturing. In the process of dividing complex product modules, components with the same or similar processes should be grouped into the same module as much as possible to improve product manufacturing efficiency. The assessment of the strength of process correlation between components is shown in Table 6, C. T (i,j) represents the strength of the process correlation between the i-th component and the j-th component.

[0103] Table 6 shows the strength of process correlation between components.

[0104]

[0105] Regarding the correlation strength of maintenance frequency, if the maintenance frequencies of components within a module differ, it will significantly increase the maintenance workload of the product. During the partitioning of complex product modules, components with similar maintenance frequencies should be grouped into the same module as much as possible to improve product maintenance efficiency. The assessment of the correlation strength of maintenance frequency between components is shown in Table 7, C. P (i,j) represents the strength of the maintenance frequency correlation between the i-th component and the j-th component.

[0106] Table 7 shows the correlation strength between maintenance frequency of components.

[0107]

[0108] Regarding the service life correlation strength, if the service lives of components within a module differ, the module may experience an increased number of failures due to the sequential failure of these components. During the modularization of complex products, components with similar or identical service lives should be grouped into the same module whenever possible to reduce product maintenance and disassembly time. The service life correlation strength assessment between components is shown in Table 8, C. L (i,j) represents the service life correlation strength between the i-th component and the j-th component.

[0109] Table 8 shows the service life correlation strength between components.

[0110]

[0111] Regarding the correlation strength of recycling methods, after a product is scrapped, its components need to be processed. The recycling methods for components mainly include reuse, material recycling, and disposal. During the modularization of complex products, components with similar recycling methods should be grouped into the same module as much as possible. This avoids the need for complete disassembly of the scrapped product, helping to improve the efficiency of product scrapping and recycling. The correlation strength assessment of recycling methods between components is shown in Table 9, C. R (i,j) represents the correlation strength of recycling methods between the i-th component and the j-th component.

[0112] Table 9 shows the correlation strength between recycling methods of components.

[0113]

[0114] The weights of the correlation strength of the eight components (i.e., the first to eighth weight coefficients) are shown in Table 10.

[0115] Table 10 shows the component correlation strength weighting table.

[0116]

[0117] Step 2: Based on the final comprehensive correlation strength matrix of components, use the core component screening method based on undirected weighted network point weight sorting to obtain multiple core components and obtain the initial core node set;

[0118] Step 2 is as follows:

[0119] First, we introduce complex network theory and construct a real undirected weighted network G based on the final comprehensive correlation strength matrix C of the components. The real undirected weighted network G is used to represent the product components and their correlation relationships, as shown in the following formula:

[0120] G = (V, E, W)

[0121] Where V represents the set of nodes in the real undirected weighted network G, i.e. all the components of the product; E represents the set of edges in the real undirected weighted network G, i.e. the relationships between the components of the product; W represents the set of edge weights in the real undirected weighted network G, where each edge weight represents the final comprehensive relationship strength between two components.

[0122] Next, the transition matrix J is established based on the edge weight set of the real undirected weighted network G, as shown in the following formula:

[0123]

[0124] Where J(i,j) represents the transition coefficient between the i-th component and the j-th component, C(i,j) represents the final comprehensive correlation strength between the i-th component and the j-th component, and α represents the correlation strength threshold. α is subjectively set through experience and satisfies 0<α<1. In this implementation, α=0.75;

[0125] Next, calculate the node weights corresponding to all components of the complex product, using the following formula:

[0126]

[0127] Among them, v r ω represents the node weight corresponding to component r. rz The weight of the z-th edge connected to the node corresponding to component r is given by g, and the total number of edges connected to the node corresponding to component r is given by g.

[0128] Finally, based on the transition matrix J and the point weights of all nodes, the core nodes corresponding to multiple core components are selected according to the Pareto principle, thereby obtaining the initial core node set. In specific implementations, the number of core components in the initial core node set is approximately 0.2n. In this implementation, the number of core components is 27.

[0129] Based on the transition matrix J and the weights of all nodes, the core nodes corresponding to multiple core components are selected according to the Pareto principle, specifically:

[0130] Sort all nodes in descending order of their weights, and select a number of nodes as core nodes in descending order of their weights. In the initial set of core nodes, the transition coefficient J(i,j) between any two core nodes and their corresponding core components is 0, that is, the correlation strength between any two core nodes and their corresponding core components cannot be greater than α.

[0131] In this embodiment, the selected core components and their corresponding node weights are shown in Table 11. The core component serial number corresponds to the component serial number in Table 1.

[0132] Table 11 is a weighted table of core components and their corresponding nodes.

[0133]

[0134]

[0135] Step 3: Based on the initial core node set, use the stable overlapping community detection algorithm based on the Shapley value determination within the community to divide the complex product into modules and obtain multiple preliminary module division schemes;

[0136] like Figure 3 As shown, step 3 specifically involves:

[0137] Step 3.1: Set the initial stability coefficient ε;

[0138] Step 3.2: Create a new empty community, denoted as B, where the community represents a module of the product; place the core node with the largest node weight in the current core node set into community B, with each core node corresponding to a core component;

[0139] Step 3.3: Subjectively set the expansion threshold δ based on experience. In a real undirected weighted network G, if the maximum edge weight connecting the inside and outside of community B (i.e., the maximum final comprehensive association strength between components inside and outside the module) C max If the number of nodes is greater than or equal to the expansion threshold δ, then community B can continue to expand, and proceed to step 3.4; otherwise, no more nodes can be added to community B to form a complete community, and proceed to step 3.11.

[0140] Step 3.4: In a real undirected weighted network G, find a node outside community B such that the edge weight between this node and a node inside community B is equal to the maximum edge weight C connecting the inside and outside of community B. max Place the node into community B, where community B may not be stable.

[0141] Step 3.5: Let the auxiliary undirected weighted network G1 be the real undirected weighted network G. At this time, the number of nodes in the current community B is set to n1.

[0142] Step 3.6: Within community B, calculate the maximum Shapley value and the Shapley value of each node in community B based on the real undirected weighted network G. According to the current stability coefficient ε and the maximum and Shapley values ​​of each node in community B, sequentially determine whether each node in community B satisfies the following inequality. If a node satisfies the following inequality, then that node affects the stability of community B, and proceed directly to step 3.7; if none of the nodes in community B satisfy the following inequality, then community B is stable, and proceed to step 3.8. The formula is as follows:

[0143]

[0144]

[0145] in, This represents the Shapley value of node i in community B. Let represent the maximum Shapley value of node i, β represent the proportion of the sum of the final comprehensive association strengths, C(i,j) represent the final comprehensive association strength between the i-th component and the j-th component, and V represent the node set of the real undirected weighted network G;

[0146] The formulas for calculating the maximum Shapley value of node i and the Shapley value of node i in community B are as follows:

[0147]

[0148]

[0149] Step 3.7: Delete the node within community B that affects the stability of community B, move the node from inside community B to outside community B, and delete the edge connecting the node to other nodes within community B from the auxiliary undirected weighted network G1. Proceed to step 3.6.

[0150] Step 3.8: If the actual number of nodes in community B is n1 at this time, go to step 3.3; otherwise, go to step 3.9.

[0151] Step 3.9: In the auxiliary undirected weighted network G1, if the maximum edge weight C connecting the inside and outside of community B is... max If the value is greater than or equal to the expansion threshold δ, then community B can continue to expand, proceed to step 3.10; otherwise, no more nodes can be added to community B to form a complete community, proceed to step 3.11.

[0152] Step 3.10: In the auxiliary undirected weighted network G1, find a node outside community B such that the edge weight between this node and a node inside community B is equal to the maximum edge weight C connecting the inside and outside of community B. max Place the node into community B. At this point, community B may not be stable. Proceed to step 3.6.

[0153] Step 3.11: Remove the core nodes that have been added to Community B from the core node set;

[0154] Step 3.12: Determine if the current core node set is empty; if the core node set is not empty, proceed to step 3.2; if the core node set is empty, multiple communities have been formed, proceed to step 3.13.

[0155] Step 3.13: Generate a preliminary module division plan based on the existing multiple communities;

[0156] Step 3.14: Change the value of the stability coefficient ε and repeat steps 3.2-3.13 to obtain preliminary module partitioning schemes corresponding to different stability coefficients ε, thereby obtaining multiple preliminary module partitioning schemes.

[0157] In this embodiment, in the stable overlapping community detection algorithm based on Shapley value determination within the community, the expansion threshold δ = 0.5 is set. By setting different stability coefficients ε, different preliminary module partitioning schemes can be generated. The three better preliminary module partitioning schemes are shown in Table 12.

[0158] Table 12 shows the preliminary scheme for the three module divisions.

[0159]

[0160]

[0161] Step 4: Optimize and select from multiple preliminary module partitioning schemes using a genetic algorithm-based overlapping component allocation method to obtain the final module partitioning scheme.

[0162] like Figure 4 As shown, step 4 specifically involves:

[0163] Step 4.1: Divide the preliminary schemes into multiple modules to form an initial first scheme set;

[0164] Step 4.2: Select any solution from the current first solution set and delete that solution from the first solution set;

[0165] Step 4.3: Determine whether there are overlapping parts between the modules in the current solution; if there are overlapping parts between the modules, proceed to step 4.4; if there are no overlapping parts between the modules, proceed to step 4.6.

[0166] Step 4.4: Filter out overlapping components in the current solution and delete these components from each module of the current solution;

[0167] Step 4.5: Use the current number of overlapping parts as the chromosome length L in the genetic algorithm, and use the genetic algorithm to assign these overlapping parts to the most suitable modules to obtain a new module partitioning scheme;

[0168] Step 4.5 specifically involves:

[0169] Step 4.5.1: Set the parameters of the genetic algorithm, namely, population size N, termination generation T, and crossover probability P. c Probability of mutation P mChromosome length L equals the number of overlapping components. The position index of a chromosome gene represents the sequence number of the overlapping component, and the numerical value in the gene represents the sequence number of the module to which that overlapping component belongs. An example of chromosome coding is shown below. Figure 5 As shown in (a); generate multiple chromosomes of fixed length, the number of chromosomes being equal to the population size N, and randomly assign an integer to each gene of the chromosome within the range of the number of modules, thereby generating the initial population;

[0170] Step 4.5.2: Calculate the fitness of each individual in the current population using the following formula;

[0171]

[0172]

[0173] Where Q represents the fitness of the genetic algorithm, i.e., the modularity metric; the larger Q is, the more reasonable the module partitioning scheme and the higher the quality of module partitioning; h represents the number of modules in the current module partitioning scheme; and e represents the module matrix. tt =y tt y tt This represents the proportion of the sum of the final comprehensive association strengths of the components within module t to the sum of the final comprehensive association strengths of all components in the product; when t ≠ u, e tu =y tu / 2,y tu This represents the proportion of the sum of the final comprehensive correlation strengths of the components between module t and module u to the sum of the final comprehensive correlation strengths of all components in the product.

[0174] Step 4.5.3: The selection operator uses roulette wheel selection. Before roulette wheel selection, the fitness of each individual is standardized using the following formula. This widens the difference in the probability of individuals being selected, thus overcoming to some extent the drawback of roulette wheel selection having a relatively large error; Q w For fitness before standardization, f w The fitness level after standardization;

[0175]

[0176] Step 4.5.4: Pair the selected N chromosomes together. For each pair of chromosomes, randomly generate a random number greater than or equal to 0 and less than or equal to 1. If this number is less than the crossover probability P... c Then the crossover operation is performed; an example of chromosome crossover operation is shown below. Figure 5 As shown in (b). Based on the chromosome length L, a one-dimensional array of length L consisting of 0s and 1s is randomly generated; when the array element corresponding to the chromosome gene is 1, the values ​​of the two parent chromosome genes are swapped; if it is 0, no operation is performed.

[0177] Step 4.5.5: Mutation Operation

[0178] like Figure 6 As shown, step 4.5.5 specifically involves:

[0179] Step 4.5.5.1: Calculate the total number of chromosomes that need to mutate, which is equal to the population size N multiplied by the mutation probability P. m And round up to +∞;

[0180] Step 4.5.5.2: For each chromosome that needs to be mutated, calculate the total number of genes that need to be mutated, which is equal to the chromosome length L multiplied by the mutation probability P. m Rounding up to +∞ helps to distribute the mutated genes more evenly.

[0181] Step 4.5.5.3: Randomly select a chromosome that needs to be mutated;

[0182] Step 4.5.5.4: Randomly select a gene from the selected chromosomes that needs to be mutated;

[0183] Step 4.5.5.5: Complete the mutation operation for this gene;

[0184] Step 4.5.5.6: Example of chromosome variation operation as follows Figure 5 As shown in (c), the chromosome is judged to have completed the mutation by whether the number of mutated genes in the chromosome reaches the total number of genes that the chromosome needs to mutate; if the chromosome has not completed the mutation, proceed to step 4.5.5.4; if the chromosome has completed the mutation, proceed to step 4.5.5.7.

[0185] Step 4.5.5.7: Determine whether the population has completed the mutation by checking whether the number of mutated chromosomes has reached the total number of chromosomes that need to be mutated; if the population has not completed the mutation, proceed to step 4.5.5.3; if the population has completed the mutation, end the mutation operation process and proceed to step 4.5.6.

[0186] Step 4.5.6: Determine if the genetic algorithm has reached the termination generation number T; if it has reached the termination generation number T, proceed to step 4.5.7; if it has not reached the termination generation number T, proceed to step 4.5.2.

[0187] Step 4.5.7: Based on the results of the genetic algorithm, select the optimal solution, that is, which modules the overlapping parts should be assigned to. Complete the assignment of overlapping parts in the current scheme according to the optimal solution, thereby obtaining a new module partitioning scheme.

[0188] Step 4.6: Add the current solution to the second solution set as a candidate solution for module partitioning;

[0189] Step 4.7: Determine if there are any remaining solutions in the first solution set; if there are remaining solutions, proceed to step 4.2; if there are no remaining solutions, proceed to step 4.8.

[0190] Step 4.8: By comparing the modularity metric Q of each module partitioning candidate scheme in the second scheme set, the module partitioning candidate scheme with the largest modularity metric Q is taken as the final module partitioning scheme.

[0191] For the three preliminary module partitioning schemes above, if there are overlapping parts between modules, these parts are first identified and then removed from each module. A genetic algorithm is used to assign these overlapping parts to the most suitable modules, and the parameters of the genetic algorithm are shown in Table 13. If there are no overlapping parts between modules, the preliminary module partitioning scheme is considered a candidate module partitioning scheme. The three candidate module partitioning schemes are shown in Table 14. It can be seen that scheme 3 has the largest modularity metric value Q, so scheme 3 is selected as the final module partitioning scheme for the CNC grinding machine.

[0192] Table 13 shows the parameter settings for the genetic algorithm.

[0193]

[0194] Table 14 lists the three candidate schemes for module partitioning.

[0195]

[0196] Finally, it should be noted that the above embodiments and descriptions are only used to illustrate the technical solutions of the present invention and not to limit it. Those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the disclosure of the technical solutions of the present invention, and all such modifications and substitutions should be covered within the protection scope of the claims of the present invention.

Claims

1. A method for dividing complex product modules based on multi-component correlation analysis, characterized in that, Includes the following steps: Step 1: Establish a comprehensive correlation strength matrix for components from the perspective of the entire product lifecycle; Step 2: Based on the final comprehensive correlation strength matrix of components, use the core component screening method based on undirected weighted network point weight sorting to obtain multiple core components and obtain the initial core node set; Step 3: Based on the initial core node set, use the stable overlapping community detection algorithm based on the Shapley value determination within the community to divide the complex product into modules and obtain multiple preliminary module division schemes; Step 3 specifically involves: Step 3.1: Set the initial stability coefficient ε; Step 3.2: Create a new empty community, denoted as B, where the community represents a module of the product; place the core node with the highest node weight in the current core node set into community B; Step 3.3: In a real undirected weighted network G, if the maximum edge weight C connecting the inside and outside of community B is... max If the number of nodes is greater than or equal to the expansion threshold δ, then community B can continue to expand, and proceed to step 3.4; otherwise, no more nodes can be added to community B to form a complete community, and proceed to step 3.

11. Step 3.4: In a real undirected weighted network G, find a node outside community B such that the edge weight between this node and a node inside community B is equal to the maximum edge weight C connecting the inside and outside of community B. max Place the node in community B; Step 3.5: Let the auxiliary undirected weighted network G1 be the real undirected weighted network G. At this time, the number of nodes in the current community B is set to n1. Step 3.6: Within community B, calculate the maximum Shapley value and the Shapley value of each node in community B based on the real undirected weighted network G. According to the current stability coefficient ε and the maximum and Shapley values ​​of each node in community B, sequentially determine whether each node in community B satisfies the following inequality. If a node satisfies the following inequality, then that node affects the stability of community B, and proceed directly to step 3.7; if none of the nodes in community B satisfy the following inequality, then community B is stable, and proceed to step 3.

8. The formula is as follows: in, This represents the Shapley value of node i in community B. Let represent the maximum Shapley value of node i, β represent the proportion of the sum of the final comprehensive association strengths, C(i, j) represent the final comprehensive association strength between the i-th component and the j-th component, and V represent the node set of the real undirected weighted network G; Step 3.7: Delete the node within community B that affects the stability of community B, move the node from inside community B to outside community B, and delete the edge connecting the node to other nodes within community B from the auxiliary undirected weighted network G1. Proceed to step 3.

6. Step 3.8: If the actual number of nodes in community B is n1 at this time, go to step 3.3; otherwise, go to step 3.

9. Step 3.9: In the auxiliary undirected weighted network G1, if the maximum edge weight C connecting the inside and outside of community B is... max If the value is greater than or equal to the expansion threshold δ, then community B can continue to expand, proceed to step 3.10; otherwise, no more nodes can be added to community B to form a complete community, proceed to step 3.

11. Step 3.10: In the auxiliary undirected weighted network G1, find a node outside community B such that the edge weight between this node and a node inside community B is equal to the maximum edge weight C connecting the inside and outside of community B. max Place the node in community B and proceed to step 3.6; Step 3.11: Remove the core nodes that have been added to Community B from the core node set; Step 3.12: Determine if the current core node set is empty; if the core node set is not empty, proceed to step 3.

2. If the core node set is empty, then multiple communities have been formed, proceed to step 3.13; Step 3.13: Generate a preliminary module division plan based on the existing multiple communities; Step 3.14: Change the value of the stability coefficient ε and repeat steps 3.2-3.13 to obtain preliminary module partitioning schemes corresponding to different stability coefficients ε, thereby obtaining multiple preliminary module partitioning schemes; Step 4: Optimize and select multiple preliminary module partitioning schemes using a genetic algorithm-based overlapping component allocation method to obtain the final module partitioning scheme.

2. The method for dividing complex product modules based on multi-component correlation analysis according to claim 1, characterized in that, In step 1, the final comprehensive correlation strength matrix C of the components is a correlation strength sub-matrix C based on customer requirements. N Functional correlation strength submatrix C F Structural correlation strength submatrix C S Material category correlation strength submatrix C M Process correlation strength submatrix C T , Maintaining the frequency correlation strength submatrix C P Lifetime correlation strength submatrix C L The correlation strength submatrix C with the recycling method R Obtained through calculation.

3. The method for dividing complex product modules based on multi-component correlation analysis according to claim 1, characterized in that, Step 1 specifically involves: First, the customer demand correlation strength submatrix C N Functional correlation strength submatrix C F Structural correlation strength submatrix C S Material category correlation strength submatrix C M Process correlation strength submatrix C T , Maintaining the frequency correlation strength submatrix C P Lifetime correlation strength submatrix C L The correlation strength submatrix C with the recycling method R After weighted summation, the component comprehensive correlation strength matrix C1 in fuzzy number form is obtained, and the calculation formula is as follows: Where S1-S8 are the first to eighth weight coefficients, respectively, 1 ≤ i ≤ n, 1 ≤ j ≤ n, n is the total number of parts in the complex product, and C N (i, j) represents the customer demand correlation strength between the i-th component and the j-th component, C F (i, j) represents the functional association strength between the i-th component and the j-th component, C S (i, j) represents the structural correlation strength between the i-th component and the j-th component, C M (i, j) represents the material category association strength between the i-th component and the j-th component, C T (i, j) represents the process correlation strength between the i-th component and the j-th component, C P (i, j) represents the maintenance frequency correlation strength between the i-th component and the j-th component, C L (i, j) represents the service life correlation strength between the i-th component and the j-th component, C R (i, j) represents the correlation strength of the recycling methods between the i-th component and the j-th component; Next, the component comprehensive correlation strength matrix C1 in fuzzy number form is converted into the component comprehensive correlation strength matrix C2 in real number form. After standardizing the component comprehensive correlation strength matrix C2 in real number form, the final comprehensive correlation strength matrix C is obtained.

4. The method for dividing complex product modules based on multi-component correlation analysis according to claim 1, characterized in that, Step 2 specifically involves: First, we introduce complex network theory and construct a real undirected weighted network G based on the final comprehensive correlation strength matrix C of the components, as shown in the following formula: Where V represents the set of nodes in the real undirected weighted network G, where each node represents a component of the product; E represents the set of edges in the real undirected weighted network G, where each edge represents the relationship between two components; and W represents the set of edge weights in the real undirected weighted network G, where each edge weight represents the final comprehensive relationship strength between two components. Next, the transition matrix J is established based on the edge weight set of the real undirected weighted network G, as shown in the following formula: Where J(i, j) represents the transition coefficient between the i-th component and the j-th component, C(i, j) represents the final comprehensive correlation strength between the i-th component and the j-th component, and α represents the correlation strength threshold; Next, calculate the node weights corresponding to all components of the complex product, using the following formula: Among them, v r ω represents the node weight corresponding to component r. rz The weight of the z-th edge connected to the node corresponding to component r is given by g, and the total number of edges connected to the node corresponding to component r is given by g. Finally, based on the transition matrix J and the point weights of all nodes, the core nodes corresponding to multiple core components are selected according to the Pareto principle, thereby obtaining the initial core node set.

5. The method for dividing complex product modules based on multi-component correlation analysis according to claim 3, characterized in that, The process involves using the transition matrix J and the point weights of all nodes to select core nodes corresponding to multiple core components according to the Pareto principle, specifically as follows: Several nodes are selected as core nodes in descending order of their point weights, and the transition coefficient J(i, j) between any two core nodes and their corresponding core components is 0.

6. The method for dividing complex product modules based on multi-component correlation analysis according to claim 1, characterized in that, Step 4 specifically involves: Step 4.1: Divide the preliminary schemes into multiple modules to form an initial first scheme set; Step 4.2: Select any solution from the current first solution set and delete that solution from the first solution set; Step 4.3: Determine whether there are overlapping parts between the modules in the current solution; if there are overlapping parts between the modules, proceed to step 4.4; if there are no overlapping parts between the modules, proceed to step 4.

6. Step 4.4: Filter out overlapping components in the current solution and delete these components from each module of the current solution; Step 4.5: Use the current number of overlapping parts as the chromosome length L in the genetic algorithm, and use the genetic algorithm to assign these overlapping parts to the most suitable modules to obtain a new module partitioning scheme; Step 4.6: Add the current solution to the second solution set as a candidate solution for module partitioning; Step 4.7: Determine if there are any remaining solutions in the first solution set; if there are remaining solutions, proceed to step 4.2; if there are no remaining solutions, proceed to step 4.

8. Step 4.8: By comparing the modularity metric Q of each module partitioning candidate scheme in the second scheme set, the module partitioning candidate scheme with the largest modularity metric Q is taken as the final module partitioning scheme.

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