Production line parameter change propagation evolution modeling method based on hypergraph theory

Abstract

A production line parameter change propagation evolution modeling method based on a hypergraph theory comprises the following steps: S1, hypergraph modeling: constructing a hypergraph model by taking a set of cross-dimension parameter nodes, hyperedges in dimensions, weights of the hyperedges and a constraint function set associated with the hyperedges as parameters; s2, parameter evolution: evolution is carried out on a production line parameter network based on a hypergraph theory, evolution means comprise parameter deconstruction and splitting, parameter fusion and aggregation, parameter derivation and inheritance, cross-dimension parameter synchronous updating and parameter resetting triggered by constraints, and one or more of the modes are selected according to conditions of production line parameters; and S3, evolution change modeling: setting a deformation operation triggering mode, and setting parameter evolution change modeling. According to the method, mathematical modeling is carried out on production line parameter association change propagation and dynamic evolution by adopting the hypergraph theory, and complex relations, dynamic changes and mutual influences in the production line can be described and analyzed more accurately.

Description

Technical Field

[0001] The present invention relates to the technical field related to data modeling and analysis, and in particular to a production line parameter change propagation evolution modeling method based on hypergraph theory. Background Art

[0002] The complexity and high degree of integration of production lines create close interdependencies between various process steps, equipment parameters, quality control, and other factors. When a production line parameter changes, the change is not limited to a specific step but can affect other parts through internal system dependencies. Therefore, accurately understanding and predicting the propagation effects of changes can provide strong support for production line optimization, problem prediction, and management decision-making.

[0003] Production lines typically involve multiple process links and equipment, and parameter changes in each link may interact through various means such as material flow, energy flow, and information flow. Mathematical modeling can quantify these changes and predict their impact on the performance of the entire production line. The dynamic evolution of the production line requires us to be able to track and predict the long-term impact of parameter changes on the production process. During the production process, factors such as equipment aging, technology upgrades, and changes in demand will continuously lead to changes in production parameters. These changes may be gradual or sudden. Through dynamic system modeling, these changes can be incorporated into the model, considering how the system evolves over time, and ensuring that the production line can maintain high efficiency and reliability in the face of external disturbances.

[0004] Optimizing and improving production lines relies on timely responses and adjustments to various changes. Mathematical modeling provides decision makers with a data-driven tool to help them understand the potential impact of parameter changes and develop appropriate adjustment strategies. For example, optimization methods from control theory can be used to adjust production line operating parameters in real time after a change occurs to maintain optimal production conditions and avoid performance degradation or resource waste.

[0005] The complexity of a production line isn't limited to a single production process or piece of equipment; it involves the coordinated work of multiple systems and processes. Current technologies primarily focus on modeling a single process or piece of equipment, lacking cross-process and cross-system collaborative modeling. For example, the interactions and dependencies between a production line's logistics system, quality control system, and equipment maintenance system are often not fully modeled and considered, limiting overall efficiency and optimization.

[0006] Existing technologies often require considering multiple variables and complex interrelationships within a production line, resulting in highly complex models. For large-scale production lines, the numerous parameters, equipment, and processes involved require extensive computational and analytical effort to construct an accurate mathematical model. Especially when considering parameter correlations and dynamic evolution, the model may involve numerous nonlinear, time-varying, and random factors, making it extremely difficult to solve. Complex models can lead to low computational efficiency and even make real-time predictions and optimization impossible. Summary of the Invention

[0007] To address the above-mentioned shortcomings, the present invention adopts hypergraph theory to mathematically model the propagation and dynamic evolution of production line parameter association changes, which can more accurately describe and analyze the complex relationships, dynamic changes and their mutual influence in the production line.

[0008] To achieve this object, the present invention adopts the following technical solutions:

[0009] A production line parameter change propagation evolution modeling method based on hypergraph theory includes the following steps:

[0010] S1. Hypergraph modeling: A hypergraph model is constructed with the set of cross-dimensional parameter nodes, hyperedges within a dimension, hyperedge weights, and the set of constraint functions associated with hyperedges as parameters.

[0011] S2. Parameter evolution: Based on hypergraph theory, the production line parameter network is evolved. Evolution methods include parameter deconstruction and splitting, parameter fusion and aggregation, parameter derivation and inheritance, cross-dimensional parameter synchronization update, and constraint-triggered parameter reset. One or more of the above methods are selected based on the production line parameters.

[0012] S3. Evolutionary change modeling, setting the variant operation triggering method, and setting parameter evolutionary change modeling.

[0013] Preferably, the step S1 specifically includes:

[0014] The production line parameter network is a hypergraph: H = (V, ε, W, F)

[0015] Cross-dimensional parameter node set, V k is the k-th dimension parameter, and the dimensions are configuration dimension, behavior dimension, control dimension, and execution dimension;

[0016] ε=ε intra ∪ε inter :ε intra is the hyperedge within the dimension, such as the logical coupling of behavioral parameters; ε inter It is a cross-dimensional hyperedge, such as the correlation effect between behavior parameters and control parameters;

[0017] W: ε→[0,1]: represents the weight of the hyperedge, indicating the coupling strength;

[0018] F: ε→g: set of constraint functions associated with hyperedge, g(e p ≤0) indicates the physical constraints between parameters.

[0019] Preferably, in step S2, specifically:

[0020] S21. Deconstruction and splitting of parameters: decomposing a single parameter into multiple sub-parameters to form hierarchical dependencies. The mathematical model is:

[0021] Original parameter: v parent ∈V;

[0022] Sub-parameter set: v child1 ,v child2 ,…,v childs ;

[0023] Deconstructing the hyperedge: e split ={v parent ,v child1 ,…,v childs};

[0024] Constraint equation: v parent =f split (v child1 ,...,v childs );

[0025] S22, parameter fusion and aggregation, multiple parameters are merged into new parameters, the mathematical model is:

[0026] Fusion parameter: v fused =f fuse (v1,…,v s );

[0027] Aggregate hyperedge: e fused ={v1,...,v s ,v fused};

[0028] S23, parameter derivation and inheritance, parameters generate new parameters through rules, forming a derivation chain or inheritance tree, the mathematical model is:

[0029] Parent parameter: v base ;

[0030] Derived parameter: v derived =f derive (v base ,θ), where θ is the derived parameter;

[0031] Derived hyperedge: e derive ={vbase ,v derived}, weight (derived strength);

[0032] S24. Cross-dimensional parameters are updated synchronously. Parameters in different dimensions need to be updated in a linked manner due to logical dependencies. The mathematical model is:

[0033] Cross-layer hyperedge: e sync ={v dim1 ,v dim2}∈ε inter ;

[0034] Synchronous equation: v dim2 =h(v dim1 );

[0035] S25, constraint-triggered parameter reset, forced adjustment when parameters violate physical or logical constraints, the mathematical model is:

[0036] Constraints: g(v1,…,v s )≤0;

[0037] Reset rule: If g>0, then

[0038] Furthermore, in step S3, the following steps are included:

[0039] S31, Formal definition of variant operation;

[0040] Let the transformation operation O be a quaternion:

[0041] O=(Trigger,ΔV,Δε,ΔW);

[0042] Trigger is the operation triggering condition, including manual instructions and system events;

[0043] ΔV is the node addition and deletion set, ΔV + For the new, ΔV - To delete;

[0044] Δε is the set of hyperedge additions and deletions;

[0045] ΔW: Weight adjustment set.

[0046] Furthermore, in step S3, the following steps are included:

[0047] S32, dynamic rules for hyperedge updates;

[0048] S321. Direct transmission:

[0049] If operation O modifies node v i , then traverse all the iThe hyperedge e p , trigger weight update: Z is the system loss function, γ is the learning rate;

[0050] S322. Indirect transmission:

[0051] Calculate multi-level influence through the hypergraph adjacency tensor A, Δε (t+1) =A (t) Δε (t) ;

[0052] Among them, the hypergraph adjacency tensor A = dimension |V|×|ε|×|W|.

[0053] In addition, step S3 includes the following steps:

[0054] S33, Hypergraph Evolution Equation;

[0055] V (t+1) =V (t) ∪ΔV + \ΔV - ;

[0056] ε (t+1) =(ε(t)\Δε - )∪ΔVε + ;

[0057] Among them, V (t+1) is the number of nodes within T+1 time; ε (t+1) is the number of edges in time T+1; ε is the number of edges; V is the number of nodes.

[0058] One of the above technical solutions includes the following beneficial effects: The present invention utilizes hypergraph theory to mathematically model the propagation and dynamic evolution of production line parameter association changes, enabling a more accurate description and analysis of complex relationships, dynamic changes, and their mutual influence within the production line. The advantages of hypergraphs lie in their ability to express many-to-many relationships, adapt to dynamic evolution, facilitate cross-system collaborative modeling, and handle complex dependencies. This makes hypergraph theory a powerful tool for addressing the complexity and dynamic changes in modern production line management, providing new insights and methods for production optimization, change management, and decision support. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a schematic diagram of the overall process of the present invention;

[0060] Figure 2 It is a schematic diagram of the method steps of parameter evolution of the present invention;

[0061] Figure 3It is a schematic diagram of the steps of the hyperedge update dynamic rule of the present invention. DETAILED DESCRIPTION

[0062] The following describes embodiments of the present invention in detail. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended only to explain the present invention and are not to be construed as limiting the present invention.

[0063] like Figure 1 As shown, a production line parameter change propagation evolution modeling method based on hypergraph theory includes the following steps:

[0064] S1. Hypergraph modeling: A hypergraph model is constructed with the set of cross-dimensional parameter nodes, hyperedges within a dimension, hyperedge weights, and the set of constraint functions associated with hyperedges as parameters.

[0065] S2. Parameter evolution: Based on hypergraph theory, the production line parameter network is evolved. Evolution methods include parameter deconstruction and splitting, parameter fusion and aggregation, parameter derivation and inheritance, cross-dimensional parameter synchronization update, and constraint-triggered parameter reset. One or more of the above methods are selected based on the production line parameters.

[0066] S3. Evolutionary change modeling, setting the variant operation triggering method, and setting parameter evolutionary change modeling.

[0067] This paper uses hypergraph theory to mathematically model the propagation and dynamic evolution of production line parameter association changes, enabling a more precise description and analysis of complex relationships, dynamic changes, and their mutual influence within the production line. The advantages of hypergraphs lie in their ability to express many-to-many relationships, adapt to dynamic evolution, facilitate cross-system collaborative modeling, and handle complex dependencies. This makes hypergraph theory a powerful tool for addressing the complexity and dynamic changes in modern production line management, providing new insights and methods for production optimization, change management, and decision support.

[0068] Wherein, the step S1 is specifically as follows:

[0069] The production line parameter network is a hypergraph: H = (V, ε, W, F)

[0070] Cross-dimensional parameter node set, V k is the k-th dimension parameter, and the dimensions are configuration dimension, behavior dimension, control dimension, and execution dimension;

[0071] ε=ε intra ∪ε inter :ε intrais the hyperedge within the dimension, such as the logical coupling of behavioral parameters; ε inter It is a cross-dimensional hyperedge, such as the correlation effect between behavior parameters and control parameters;

[0072] W: ε→[0,1]: represents the weight of the hyperedge, indicating the coupling strength;

[0073] F: ε→g: set of constraint functions associated with hyperedge, g(e p ≤0) indicates the physical constraints between parameters.

[0074] Traditional graph models (such as ordinary directed graphs) can only represent binary relationships between two nodes, while the associations between production line parameters often show the characteristics of many-to-many, synergistic effects, and cross-dimensional coupling. Hyperedge modeling: A hyperedge can simultaneously connect multiple input nodes (cause parameters) and multiple output nodes (result parameters). Avoid information fragmentation: There is no need to decompose complex associations into multiple binary edges, reducing model redundancy and logical faults. Production line parameters are distributed in the four dimensions of "configuration-behavior-control-execution". Traditional methods require hierarchical modeling, which makes it difficult to capture direct cross-dimensional effects. Hyperedges can directly connect parameters of different dimensions without the need for intermediate conversion. Execution dimension parameters can reversely affect control parameters through hyperedges, supporting dynamic closed-loop control logic. Production line parameters may increase or decrease dynamically with process iterations, and the hypergraph model can adapt to changes by flexibly adjusting hyperedges and nodes.

[0075] Incremental modeling: Adding new parameters requires only adding nodes and associated hyperedges, without reconstructing the entire network. Heterogeneous attribute support: Nodes can be assigned multiple attributes (such as speed, location, cost weight, etc.), and hyperedges can define dynamic functions (such as integrals and differential equations) to directly map physical or logical relationships between parameters.

[0076] Configuration: This focuses primarily on the physical planning and configuration of the production line. It involves determining the overall structure of the production line based on product production needs, process requirements, and resource allocation. Configuration design encompasses not only the selection and placement of equipment but also the connections between equipment, transmission paths, and workstation configuration.

[0077] Behavior: This focuses on the coordination and planning of the movements of various work units and equipment within the production line. Specifically, it refers to how to rationally arrange various tasks (such as equipment startup, operation, transfer, and shutdown) to ensure a smooth and efficient production process. In the design of dynamics, factors such as the working sequence of each device, task scheduling, and action timing must be considered to avoid unnecessary waiting and conflicts.

[0078] Control: This aims to enable information exchange and coordinated control between various devices and workstations on the production line. The core of control design lies in the precise interaction between information systems and physical devices. This includes the construction of control networks, data collection and analysis, decision-making, and command issuance. Effective control design enables automated production line monitoring, real-time scheduling, and feedback adjustments, thereby enhancing the flexibility and responsiveness of the production process. The seamless connection between the information and physical worlds makes the entire production process more intelligent and adaptive.

[0079] Execution: Execution is the core of the production line optimization process. It achieves optimal production operations by optimizing the entire line's drive engine. Execution focuses on precisely controlling every aspect of the production line through multi-dimensional data analysis and model optimization to achieve the optimal balance between production efficiency, quality, and cost. This involves optimization in multiple areas, from production scheduling to equipment maintenance, from energy management to quality control.

[0080] like Figure 2 As shown, in step S2, specifically:

[0081] S21. Deconstruction and splitting of parameters: decomposing a single parameter into multiple sub-parameters to form hierarchical dependencies. The mathematical model is:

[0082] Original parameter: v parent ∈V;

[0083] Sub-parameter set: v child1 ,v child2 ,…,v childs ;

[0084] Deconstructing the hyperedge: e split ={v parent ,v child1 ,…,v childs};

[0085] Constraint equation: v parent =f split (v child1 ,...,v childs );

[0086] S22, parameter fusion and aggregation, multiple parameters are merged into new parameters, the mathematical model is:

[0087] Fusion parameter: v fused =f fuse (v1,…,v s );

[0088] Aggregate hyperedge: e fused ={v1,...,v s ,v fused};

[0089] S23, parameter derivation and inheritance, parameters generate new parameters through rules, forming a derivation chain or inheritance tree, the mathematical model is:

[0090] Parent parameter: v base ;

[0091] Derived parameter: v derived =f derive (v base ,θ), where θ is the derived parameter;

[0092] Derived hyperedge: e derive ={v base ,v derived}, weight (derived strength);

[0093] S24. Cross-dimensional parameters are updated synchronously. Parameters in different dimensions need to be updated in a linked manner due to logical dependencies. The mathematical model is:

[0094] Cross-layer hyperedge: e sync ={v dim1 ,v dim2}∈ε inter ;

[0095] Synchronous equation: v dim2 =h(v dim1 );

[0096] S25, constraint-triggered parameter reset, forced adjustment when parameters violate physical or logical constraints, the mathematical model is:

[0097] Constraints: g(v1,…,v s )≤0;

[0098] Reset rule: If g>0, then

[0099] In addition, step S3 includes the following steps:

[0100] S31, Formal definition of variant operation;

[0101] Let the transformation operation O be a quaternion:

[0102] O=(Trigger,ΔV,Δε,ΔW);

[0103] Trigger is the operation triggering condition, including manual instructions and system events;

[0104] ΔV is the node addition and deletion set, ΔV + For the new, ΔV - To delete;

[0105] Δε is the set of hyperedge additions and deletions;

[0106] ΔW: Weight adjustment set.

[0107] This is a mathematical representation of the evolution of parameters when a production line is modified, using mathematical modeling to characterize the evolution process. The production line needs to change the product, replace a functional device, or change from manual to equipment.

[0108] In addition, step S3 includes the following steps:

[0109] like Figure 3 As shown, S32, dynamic rules for hyperedge updating;

[0110] S321. Direct transmission:

[0111] If operation O modifies node v i , then traverse all the i The hyperedge e p , trigger weight update: Z is the system loss function, γ is the learning rate;

[0112] S322. Indirect transmission:

[0113] Calculate multi-level influence through the hypergraph adjacency tensor A, Δε (t+1) =A (t) Δε (t) ;

[0114] Among them, the hypergraph adjacency tensor A = dimension |V|×|ε|×|W|.

[0115] Production line modifications can propagate parameter changes through indirect or direct propagation. Mathematical modeling is a new concept. There's no specific precedence for direct or indirect propagation; the decision is based on actual conditions.

[0116] In addition, step S3 includes the following steps:

[0117] S33, Hypergraph Evolution Equation;

[0118] V (t+1) =V (t) ∪ΔV + \ΔV - ;

[0119] ε (t+1) =(ε (t) \Δε - )∪ΔVε + ;

[0120] Among them, V (t+1) is the number of nodes within T+1 time; ε(t+1) is the number of edges in time T+1; ε is the number of edges; V is the number of nodes.

[0121] The technical principles of the present invention have been described above with reference to specific embodiments. These descriptions are intended solely to illustrate the principles of the present invention and are not to be construed in any way as limiting the scope of protection of the present invention. Based on the explanations herein, those skilled in the art will readily conceive of other specific embodiments of the present invention without inventive effort, and such embodiments will fall within the scope of protection of the present invention.

Claims

1. A production line parameter change propagation evolution modeling method based on hypergraph theory, characterized by: The following steps are involved: S1. Hypergraph modeling: A hypergraph model is constructed with the set of cross-dimensional parameter nodes, hyperedges within a dimension, hyperedge weights, and the set of constraint functions associated with hyperedges as parameters. S2. Parameter evolution: Based on hypergraph theory, the production line parameter network is evolved. Evolution methods include parameter deconstruction and splitting, parameter fusion and aggregation, parameter derivation and inheritance, cross-dimensional parameter synchronization update, and constraint-triggered parameter reset. One or more of the above methods are selected based on the production line parameters. S3. Evolutionary change modeling, setting the variant operation triggering method, and setting the parameter evolutionary change modeling.

2. The production line parameter change propagation evolution modeling method based on hypergraph theory according to claim 1 is characterized in that: In the step S1, specifically: The production line parameter network is a hypergraph: H = (V, ε, W, F) Cross-dimensional parameter node set, V k is the k-th dimension parameter, and the dimensions are configuration dimension, behavior dimension, control dimension, and execution dimension; ε=ε intra ∪ε inter :ε intra is the hyperedge within the dimension, such as the logical coupling of behavioral parameters; ε inter It is a cross-dimensional hyperedge, such as the correlation effect between behavior parameters and control parameters; W: ε→[0,1]: represents the weight of the hyperedge, indicating the coupling strength; F: ε→g: set of constraint functions associated with hyperedge, g(e p ≤0) indicates the physical constraints between parameters.

3. The production line parameter change propagation evolution modeling method based on hypergraph theory according to claim 2 is characterized in that: In step S2, specifically: S21. Deconstruction and splitting of parameters: decomposing a single parameter into multiple sub-parameters to form hierarchical dependencies. The mathematical model is: Original parameter: v parent ∈V; Sub-parameter set: v child1 ,v child2 ,…,v childs ; Deconstructing the hyperedge: e split ={v parent ,v child1 ,…,v childs }; Constraint equation: v parent =f split (v child1 ,...,v childs ); S22, parameter fusion and aggregation, multiple parameters are merged into new parameters, the mathematical model is: Fusion parameter: v fused =f fuse (v1,…,v s ); Aggregate hyperedge: e fused ={v1,...,v s ,v fused }; S23, parameter derivation and inheritance, parameters generate new parameters through rules, forming a derivation chain or inheritance tree, the mathematical model is: Parent parameter: v base ; Derived parameter: v derived =f derive (v base ,θ), where θ is the derived parameter; Derived hyperedge: e derive ={v base ,v derived }, weight (derived strength); S24. Cross-dimensional parameters are updated synchronously. Parameters in different dimensions need to be updated in a linked manner due to logical dependencies. The mathematical model is: Cross-layer hyperedge: e sync ={v dim1 ,v dim2 }∈ε inter ; Synchronous equation: v dim2 =h(v dim1 ); S25, constraint-triggered parameter reset, forced adjustment when parameters violate physical or logical constraints, the mathematical model is: Constraints: g(v1,…,v s )≤0; Reset rule: If g>0, then stg≤0.

4. The production line parameter change propagation evolution modeling method based on hypergraph theory according to claim 3 is characterized in that: In step S3, the following steps are included: S31, Formal definition of variant operation; Let the transformation operation O be a quaternion: O=(Trigger,ΔV,Δε,ΔW); Trigger is the operation triggering condition, including manual instructions and system events; ΔV is the node addition and deletion set, ΔV + For the new, ΔV - To delete; Δε is the set of hyperedge additions and deletions; ΔW: Weight adjustment set.

5. The production line parameter change propagation evolution modeling method based on hypergraph theory according to claim 4 is characterized in that: In step S3, the following steps are included: S32, dynamic rules for hyperedge updates; S321. Direct transmission: If operation O modifies node v i , then traverse all the i The hyperedge e p , trigger weight update: Z is the system loss function, γ is the learning rate; S322. Indirect transmission: Calculate multi-level influence through the hypergraph adjacency tensor A, Δε (t+1) =A (t) Δε (t) ; Among them, the hypergraph adjacency tensor A = dimension |V|×|ε|×|W|.

6. The production line parameter change propagation evolution modeling method based on hypergraph theory according to claim 5 is characterized in that: In step S3, the following steps are included: S33, Hypergraph Evolution Equation; V (t+1) =V (t) ∪ΔV + \ΔV - ; e (t+1) =(e (t) \No - )∪ΔVε + ; Among them, V (t+1) is the number of nodes within T+1 time; ε (t+1) is the number of edges in time T+1; ε is the number of edges; V is the number of nodes.

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