A Stability Analysis Method for a Production Line Hypergraph Modeling System

Abstract

This invention discloses a stability analysis method for a production line hypergraph modeling system, comprising the following steps: First, a safety set is introduced and a baseline hypergraph state is obtained; then, a perturbation is applied to the baseline hypergraph state; next, an internal propagation mechanism is used to iteratively update the perturbed hypergraph state until the potential function of the hypergraph state after iteration satisfies the system convergence condition, allowing the system to enter the safety set; then, the hypergraph state entering the safety set is mapped to the parameter vector space, the equilibrium state of the internal propagation process is solved, and local linearization is performed to obtain the propagation matrix; finally, the spectral radius of the propagation matrix is ​​calculated, and the system stability is quantitatively determined accordingly. This invention solves the problems of existing parameter change impact assessment methods based on production line hypergraph modeling, which rely heavily on traditional low-order relational models, making it difficult to quantitatively characterize system stability, lacking calculable criteria, and failing to meet the accurate assessment needs of modern production lines for the impact of parameter changes.

Description

Technical Field

[0001] This invention relates to the field of data analysis technology for production line hypergraph modeling systems, specifically a stability analysis method for production line hypergraph modeling systems. Background Technology

[0002] A production line is a complex system composed of multiple workstations, equipment, control units, and various quality / performance indicators. Its "configuration-behavior-control-performance" parameters are strongly coupled and have multi-level dependencies. When parameters change due to factors such as model replacement, process optimization, equipment upgrades, or control strategy adjustments, their impact typically triggers a chain reaction along the system's interconnected relationships. Therefore, in highly automated production lines, assessing the operational stability, the likelihood of propagation instability, and the risk threshold after parameter changes becomes a core challenge in change management. Current technologies typically rely on constructed production line hypergraph modeling systems for parameter change impact assessment. These systems, as mathematical modeling tools for the multi-dimensional parameter relationships of production lines, can accurately depict the complex topology and dynamic evolution of the production line. However, most existing parameter change impact assessment methods based on production line hypergraph modeling systems still depend on traditional low-order relational models, making it difficult to quantitatively characterize system stability, propagation amplification effects, and recovery capabilities. They also lack practical, calculable criteria, failing to meet the needs of modern production lines for accurate assessment of parameter change impacts. Summary of the Invention

[0003] To address the aforementioned shortcomings, this invention proposes a stability analysis method for a production line hypergraph modeling system. The aim is to solve the problems that existing parameter change impact assessment methods based on production line hypergraph modeling rely heavily on traditional low-order relational models, making it difficult to quantitatively characterize system stability and lacking calculable criteria, thus failing to meet the needs of modern production lines for accurate assessment of the impact of parameter changes.

[0004] To achieve this objective, the present invention adopts the following technical solution: A stability analysis method for a production line hypergraph modeling system includes the following steps: Step S1: Construct the safety set of the production line hypergraph modeling system And obtain the baseline hypergraph state of the production line hypergraph modeling system. ; Step S2: Check the baseline hypergraph state By applying an external change operation sequence u, the perturbed hypergraph state is obtained. ; Step S3: Use the internal propagation mechanism to process the perturbed hypergraph state. Perform iterative updates to obtain the hypergraph state after the iteration. ,in, T represents the preset maximum number of iterations; Step S4: Calculate the potential function of the hypergraph state after iteration. and judge Does the preset system convergence condition meet? If it does, then determine... The corresponding production line hypermap modeling system enters the safety set Then proceed to step S5; if the condition is not met, continue iteratively updating the current hypergraph state until the hypergraph state corresponding to the production line hypergraph modeling system enters a safe set. ; Step S5: Enter the security set The iterative hypergraph state is mapped to a predefined parameter vector space, and the equilibrium state of the internal propagation process is obtained by solving. ; Step S6: For Perform local linearization and solve for the propagation matrix M; Step S7: Calculate the spectral radius of the propagation matrix M ,in, The specific calculation formula is as follows: ; in, This represents the magnitude of the i-th eigenvalue in the propagation matrix M; Step S8: According to The stability of the production line SuperMap modeling system is quantitatively assessed. If the production line hypergraph modeling system is locally asymptotically stable, then it is determined that the system is stable. If the system fails to meet the requirements, it is determined that the production line supermap modeling system has a strong tendency to amplify coupling or a critical instability risk.

[0005] Preferably, in step S1, the safety set of the production line hypergraph modeling system... The specific mathematical expression is as follows: ; Where H represents any hypergraph state, This indicates the degree of constraint violation for any hyperedge e; This represents the local parameter vector associated with any hyperedge e; Represents the set of superedges; Represents the state of any hypergraph The kth key performance indicator derived; This represents the allowable range for the k-th key performance indicator; k represents the index of any indicator in the set of key performance indicators K. In step S2, the perturbed hypergraph state The specific mathematical expression is as follows: ; in, This represents the baseline hypergraph state of the production line hypergraph modeling system; u represents the external change operation sequence; This represents the external disturbance function.

[0006] Preferably, step S3 specifically includes the following sub-steps: Step S31: Obtain the hypergraph state after the (t-1)th iteration. And based on this state, identify the set of active superedges participating in this iteration of propagation. ,in, ; Step S32: Obtain The nth activity superedge Corresponding vertex set ,in, The specific mathematical expression is as follows: ; Where v represents any vertex; V represents the set of superedge vertices; Represents the relationship between vertex v and active hyperedge. The membership function is used to characterize the association state between the two. Step S33: According to Constructing active hyperedges Corresponding local propagation function ,in, The specific mathematical expression is as follows: ; in, Indicates the superedge of the activity Related 3D real vector space; Step S34: Extended to an extended local propagation function defined on the parameter vector space ; Step S35: Connect each active superedge Corresponding extended local propagation function The functions are composed in iterative order to form a global propagation function in the parameter vector space. ,in, The specific mathematical expression is as follows: ; Where N represents the set of active superedges The total number of active superedges in the middle; Step S36: Propagate the global function in the parameter vector space Mapping to the hypergraph state space yields the global propagation function G corresponding to the hypergraph state space; Step S37: Apply the global propagation function G corresponding to the hypergraph state space to the hypergraph state after the (t-1)th iteration. Perform propagation iterations to obtain the hypergraph state after the t-th iteration. ,in, The specific mathematical expression is as follows: .

[0007] Preferably, in step S4, the potential function of the iterated hypergraph state... The specific calculation formula is as follows: ; in, This indicates the weight corresponding to the degree of constraint violation; This indicates the weight corresponding to the performance deviation. Indicates the degree of constraint violation. The specific mathematical expression is as follows: ; in, This represents the weight of the hyperedge e; Indicates the hyperedge e in the local parameter vector The degree of violation of the constraints; If in the current hypergraph state Under the condition that the production line constraints corresponding to superedge e are fully satisfied, If in the current hypergraph state When the production line constraint condition corresponding to superedge e is not met, If in the current hypergraph state When the production line constraint corresponding to the hyperedge e is a numerical inequality constraint, ,and ,in, Let e ​​represent the inequality constraint function corresponding to the hyperedge e; Indicates the degree of performance deviation. The specific mathematical expression is as follows: ; in, Represents the set of key performance indicators; This represents the weight coefficient of the k-th key performance indicator; Indicates the current hypergraph state The actual value of the kth key performance indicator; This represents the target value of the k-th key performance indicator; The Euclidean norm is used to measure the length of a set of vectors or the distance between two state vectors.

[0008] Preferably, in step S4, the preset system convergence conditions include: as well as .

[0009] Preferably, step S5 specifically includes the following sub-steps: Step S51: Use a state mapping function to enter the safe set The iterative hypergraph state middle The vector is expanded according to a preset order to obtain an m-dimensional real vector. ,in, The specific mathematical expression is as follows: ; in, Represents the state mapping function; Step S52: Use the global propagation function in the parameter vector space right Perform propagation iterations to obtain the parameter vector state after iteration. ,in, The specific mathematical expression is as follows: ; During the propagation iteration process, when a search is conducted that satisfies " "Conditional parameter vector state" Then the state of the parameter vector It is determined to be the equilibrium state of the internal propagation process.

[0010] Preferably, in step S6, for Local linearization is performed, and the specific mathematical equation is as follows: ; in, Represents the propagation matrix; Represents higher-order infinitesimal terms; This represents the deviation norm between the current parameter vector state and the equilibrium state; The specific formula for solving the propagation matrix M is as follows: .

[0011] Preferably, the method further includes the following steps: The convergence success rate was calculated. and based on The stability of the production line hypermap modeling system is determined, including... The specific calculation formula is as follows: ; in, Indicates the total number of perturbed samples; This represents the convergence step number corresponding to the j-th perturbation sample; Indicates that the j-th perturbation sample is in the first position. The final state of propagation during the step; Indicates characteristic functions; The average number of convergence steps was calculated separately. and the maximum number of convergence steps and based on and The stability of the production line hypermap modeling system is determined, including... The specific calculation formula is as follows: ; in, This indicates that the sample set has been successfully converged; This indicates the number of elements in the successfully converged sample set; This represents the number of convergence steps corresponding to the s-th successfully converged sample; The specific calculation formula is as follows: .

[0012] The technical solution provided by this invention may include the following beneficial effects: This scheme first introduces a safety set and obtains the baseline hypergraph state, then applies a perturbation to the baseline hypergraph state. Next, an internal propagation mechanism is used to iteratively update the perturbed hypergraph state until the potential function of the hypergraph state after iteration satisfies the system convergence condition, allowing the system to enter the safety set. Then, the hypergraph state that has entered the safety set is mapped to the parameter vector space, the equilibrium state of the internal propagation process is solved, and it is locally linearized to obtain the propagation matrix. Finally, the spectral radius of the propagation matrix is ​​calculated and used as a computability criterion, enabling quantitative determination of whether the production line hypergraph modeling system can return to a state where constraints are satisfied and key performance indicators are acceptable within a finite number of steps after being perturbed, thereby meeting the needs of modern production lines for accurate assessment of the impact of parameter changes. Attached Figure Description

[0013] Figure 1 This is a flowchart illustrating the steps of a stability analysis method for a production line hypergraph modeling system. Detailed Implementation

[0014] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0015] A stability analysis method for a production line hypergraph modeling system includes the following steps: Step S1: Construct the safety set of the production line hypergraph modeling system And obtain the baseline hypergraph state of the production line hypergraph modeling system. ; Step S2: Check the baseline hypergraph state By applying an external change operation sequence u, the perturbed hypergraph state is obtained. ; Step S3: Use the internal propagation mechanism to process the perturbed hypergraph state. Perform iterative updates to obtain the hypergraph state after the iteration. ,in, T represents the preset maximum number of iterations; Step S4: Calculate the potential function of the hypergraph state after iteration. and judge Does the preset system convergence condition meet? If it does, then determine... The corresponding production line hypermap modeling system enters the safety set Then proceed to step S5; if the condition is not met, continue iteratively updating the current hypergraph state until the hypergraph state corresponding to the production line hypergraph modeling system enters a safe set. ; Step S5: Enter the security set The iterative hypergraph state is mapped to a predefined parameter vector space, and the equilibrium state of the internal propagation process is obtained by solving. ; Step S6: For Perform local linearization and solve for the propagation matrix M; Step S7: Calculate the spectral radius of the propagation matrix M ,in, The specific calculation formula is as follows: ; in, This represents the magnitude of the i-th eigenvalue in the propagation matrix M; Step S8: According to The stability of the production line SuperMap modeling system is quantitatively assessed. If the production line hypergraph modeling system is locally asymptotically stable, then it is determined that the system is stable. If the system fails to meet the requirements, it is determined that the production line supermap modeling system has a strong tendency to amplify coupling or a critical instability risk.

[0016] This solution proposes a stability analysis method for a production line hypergraph modeling system, such as... Figure 1 As shown, the first step is to construct a security set for the production line hypergraph modeling system. And obtain the baseline hypergraph state of the production line hypergraph modeling system. In this embodiment, a security set is constructed by building a production line hypergraph modeling system. This allows for the clear identification of the state boundaries of the production line hypermap modeling system within its normal and stable operating range, providing a quantitative reference standard for subsequent assessments of whether the system is out of control. By obtaining the baseline hypermap state of the production line hypermap modeling system... This allows for the identification of the original baseline state of the production line hypermap modeling system when it is undisturbed. The second step is to define the baseline hypermap state. By applying an external change operation sequence u, the perturbed hypergraph state is obtained. In this embodiment, by applying an external change operation sequence to the baseline hypergraph state, it is possible not only to simulate the disturbed state of the production line under real operating conditions, but also to serve as the starting point for subsequent stability analysis of the production line hypergraph modeling system. The third step is to use an internal propagation mechanism to process the disturbed hypergraph state. Perform iterative updates to obtain the hypergraph state after the iteration. ,in, T represents the preset maximum number of iterations. In this embodiment, by employing an internal propagation mechanism to iteratively update the hypergraph state after disturbance, the impact of changes in production line parameters can be accurately simulated as the effects propagate and evolve along the correlation relationships within the system. The fourth step is to calculate the potential function of the iterated hypergraph state. and judge Does the preset system convergence condition meet? If it does, then determine... The corresponding production line hypermap modeling system enters the safety set Then proceed to step S5; if the condition is not met, continue iteratively updating the current hypergraph state until the hypergraph state corresponding to the production line hypergraph modeling system enters a safe set. In this embodiment, the potential function of the hypergraph state after iteration is calculated. It can quantitatively characterize the degree to which the production line supermap system deviates from a stable state. By judging... Whether the preset system convergence conditions are met determines whether the production line hypergraph modeling system has entered the safe set. This enables dynamic identification and quantitative determination of the system's state after disturbance propagation. The fifth step is to enter the safe set. The iterative hypergraph state is mapped to a predefined parameter vector space, and the equilibrium state of the internal propagation process is obtained by solving. In this embodiment, by entering the security set The iterative mapping of the hypergraph state to the parameter vector space enables the transformation from complex topological state to low-dimensional parameter vector state, reducing the complexity of subsequent system stability analysis. The equilibrium state of the internal propagation process is then solved. This allows for precise location of the production line's stable operating point after experiencing parameter changes and their propagation. The sixth step is... The propagation matrix M is obtained by performing local linearization and solving. In this embodiment, the propagation matrix M is obtained by... Local linearization can approximate a nonlinear hypergraph modeling system as a linear system at the equilibrium point. By solving for the propagation matrix, the transmission weight and coupling strength of the influence of changes in various parameters of the production line can be quantitatively characterized. The seventh step is to calculate the spectral radius of the propagation matrix M. ,in, The specific calculation formula is as follows: ;in, This represents the magnitude of the i-th eigenvalue in the propagation matrix M. In this embodiment, it is calculated by measuring the spectral radius of the propagation matrix M. This provides core criteria for subsequent evaluation of the stability of the hypergraph modeling system. The eighth step is based on... The stability of the production line SuperMap modeling system is quantitatively assessed. If the production line hypergraph modeling system is locally asymptotically stable, then it is determined that the system is stable. If the production line supermap modeling system exhibits a strong coupling amplification trend or critical instability risk, then in this embodiment, the system is determined to be based on the spectral radius. The relationship with the threshold of 1 is classified and determined in a hierarchical manner. This determination mechanism can provide a clear and operable stability evaluation standard.

[0017] This scheme first introduces a safety set and obtains the baseline hypergraph state, then applies a perturbation to the baseline hypergraph state. Next, an internal propagation mechanism is used to iteratively update the perturbed hypergraph state until the potential function of the hypergraph state after iteration satisfies the system convergence condition, allowing the system to enter the safety set. Then, the hypergraph state that has entered the safety set is mapped to the parameter vector space, the equilibrium state of the internal propagation process is solved, and it is locally linearized to obtain the propagation matrix. Finally, the spectral radius of the propagation matrix is ​​calculated and used as a computability criterion, enabling quantitative determination of whether the production line hypergraph modeling system can return to a state where constraints are satisfied and key performance indicators are acceptable within a finite number of steps after being perturbed, thereby meeting the needs of modern production lines for accurate assessment of the impact of parameter changes.

[0018] Preferably, in step S1, the safety set of the production line hypergraph modeling system... The specific mathematical expression is as follows: ; Where H represents any hypergraph state, This indicates the degree of constraint violation for any hyperedge e; This represents the local parameter vector associated with any hyperedge e; Represents the set of superedges; Represents the state of any hypergraph The kth key performance indicator derived; This represents the allowable range for the k-th key performance indicator; k represents the index of any indicator in the set of key performance indicators K. In step S2, the perturbed hypergraph state The specific mathematical expression is as follows: ; in, This represents the baseline hypergraph state of the production line hypergraph modeling system; u represents the external change operation sequence; This represents the external disturbance function.

[0019] In this embodiment, a security set is defined for the production line hypergraph modeling system. This allows us to identify hypergraph states that fully satisfy constraints and whose key performance indicators are all within acceptable ranges. This is achieved by comparing the external change operation sequence u with the baseline hypergraph state. As input parameters to the external disturbance function, it can accurately characterize the objects and mechanisms of action of various disturbances in the production line, such as parameter adjustments and changes in operating conditions. (The resulting hypergraph state is shown.) It can reflect the impact of disturbances on the state of the production line hypergraph modeling system.

[0020] Preferably, step S3 specifically includes the following sub-steps: Step S31: Obtain the hypergraph state after the (t-1)th iteration. And based on this state, identify the set of active superedges participating in this iteration of propagation. ,in, ; Step S32: Obtain The nth activity superedge Corresponding vertex set ,in, The specific mathematical expression is as follows: ; Where v represents any vertex; V represents the set of superedge vertices; Represents the relationship between vertex v and active hyperedge. The membership function is used to characterize the association state between the two. Step S33: According to Constructing active hyperedges Corresponding local propagation function ,in, The specific mathematical expression is as follows: ; in, Indicates the superedge of the activity Related 3D real vector space; Step S34: Extended to an extended local propagation function defined on the parameter vector space ; Step S35: Connect each active superedge Corresponding extended local propagation function The functions are composed in iterative order to form a global propagation function in the parameter vector space. ,in, The specific mathematical expression is as follows: ; Where N represents the set of active superedges The total number of active superedges in the middle; Step S36: Propagate the global function in the parameter vector space Mapping to the hypergraph state space yields the global propagation function G corresponding to the hypergraph state space; Step S37: Apply the global propagation function G corresponding to the hypergraph state space to the hypergraph state after the (t-1)th iteration. Perform propagation iterations to obtain the hypergraph state after the t-th iteration. ,in, The specific mathematical expression is as follows: .

[0021] In this embodiment, in step S31, based on the current hypergraph state... Identify the set of active superedges This enables precise selection of hyperedges participating in the propagation process within the production line hypergraph modeling system. It's important to note that iterative propagation is not completed globally synchronously, but rather gradually achieved through local updates to the set of active hyperedges. In step S32, by obtaining... The nth activity superedge Corresponding vertex set This allows for a clear definition of the scope of the local propagation update. In step S33, an active hyperedge is constructed. Corresponding local propagation function This provides the basic units for subsequent expansion into functions of the parameter vector space and composition into a global propagation function. In step S34, by... Extended to an extended local propagation function defined on the parameter vector space This achieves dimensional unification with the global state vector. In step S35, this is achieved through each activity hyperedge. Corresponding extended local propagation function The functions are composed in iterative order to form a global propagation function in the parameter vector space. This enables the orderly integration and synergistic effect of multiple local update rules within a unified global space. In step S36, the global propagation function in the parameter vector space... Mapping to the hypergraph state space establishes a direct correlation between the abstract parameter update logic and the topological state changes of the hypergraph. In step S37, by using the global propagation function corresponding to the hypergraph state space to iteratively update the hypergraph state, dynamic simulation of the internal constraint transmission and state evolution process of the production line hypergraph modeling system can be achieved.

[0022] Preferably, in step S4, the potential function of the iterated hypergraph state... The specific calculation formula is as follows: ; in, This indicates the weight corresponding to the degree of constraint violation; This indicates the weight corresponding to the performance deviation. Indicates the degree of constraint violation. The specific mathematical expression is as follows: ; in, This represents the weight of the hyperedge e; Indicates the hyperedge e in the local parameter vector The degree of violation of the constraints; If in the current hypergraph state Under the condition that the production line constraints corresponding to superedge e are fully satisfied, If in the current hypergraph state When the production line constraint condition corresponding to superedge e is not met, If in the current hypergraph state When the production line constraint corresponding to the hyperedge e is a numerical inequality constraint, ,and ,in, Let e ​​represent the inequality constraint function corresponding to the hyperedge e; Indicates the degree of performance deviation. The specific mathematical expression is as follows: ; in, Represents the set of key performance indicators; This represents the weight coefficient of the k-th key performance indicator; Indicates the current hypergraph state The actual value of the kth key performance indicator; This represents the target value of the k-th key performance indicator; The Euclidean norm is used to measure the length of a set of vectors or the distance between two state vectors.

[0023] In this embodiment, by introducing a potential function composed of constraint violation degree and performance deviation degree, the degree of deviation of the production line hypergraph modeling system from the ideal stable state can be quantitatively and comprehensively characterized from two dimensions: constraint satisfaction and operational performance. It should be noted that... and All are positive numbers, used to adjust the relative importance of constraint recovery and performance maintenance in the overall evaluation. When in the current hypergraph state... When the production line constraint corresponding to the hyperedge e is a numerical inequality constraint, ,when At this time ;when At this time .

[0024] Preferably, in step S4, the preset system convergence conditions include: as well as In this embodiment, when This indicates that the current production line supermap modeling system is in a stable, secure state and meets performance requirements. When the potential function shows a monotonically decreasing trend, it indicates that the current production line hypergraph modeling system is gradually approaching an acceptable state.

[0025] Preferably, step S5 specifically includes the following sub-steps: Step S51: Use a state mapping function to enter the safe set The iterative hypergraph state middle The vector is expanded according to a preset order to obtain an m-dimensional real vector. ,in, The specific mathematical expression is as follows: ; in, Represents the state mapping function; Step S52: Use the global propagation function in the parameter vector space right Perform propagation iterations to obtain the parameter vector state after iteration. ,in, The specific mathematical expression is as follows: ; During the propagation iteration process, when a search is conducted that satisfies " "Conditional parameter vector state" Then the state of the parameter vector It is determined to be the equilibrium state of the internal propagation process.

[0026] In this embodiment, in step S51, the current hypergraph state is mapped using a state mapping function. Ordered unfolding transforms complex hypergraph state data into standard m-dimensional real vectors. It should be noted that the preset order is: first, execute safety interlocking type active hyperedges; then, execute action sequence type active hyperedges; and finally, execute performance aggregation type active hyperedges. In step S52, during the unfolding... During the propagation iteration process, by using As a criterion for determining the equilibrium state, it can accurately capture the critical parameter point where the internal propagation process tends to stabilize. In other embodiments, considering that parameter repair in engineering systems is usually not suitable for completely rigid instantaneous replacement, but rather for a gradual callback approach, the propagation iteration process can be further written as a damped update form: ;in, Let represent the damping coefficient of the t-th propagation iteration, when When, it indicates that the recommended values ​​from this round of propagation are fully adopted, and a rigid update is performed; when When the time is right, it means that only the correction amount generated by this round of propagation is absorbed proportionally, thereby reducing the risk of system overshoot, oscillation or back-and-forth repair.

[0027] Preferably, in step S6, for Local linearization is performed, and the specific mathematical equation is as follows: ; in, Represents the propagation matrix; Represents higher-order infinitesimal terms; This represents the deviation norm between the current parameter vector state and the equilibrium state; The specific formula for solving the propagation matrix M is as follows: .

[0028] In this embodiment, by considering the equilibrium state Local linearization is performed by introducing higher-order infinitesimal terms. , used to characterize the state of the parameter vector Approaching equilibrium When, relative to the deviation norm Higher-order minor quantities. Under the premise of reasonably neglecting higher-order nonlinear perturbations, the local dynamic characteristics of the nonlinear discrete propagation system near the equilibrium point are accurately characterized in linear form. The propagation matrix M is specifically the value of the parameter vector state... Equivalent to equilibrium state At that time, the global propagation function For parameter vector state The Jacobian matrix.

[0029] Preferably, the following steps are also included: The convergence success rate was calculated. and based on The stability of the production line hypermap modeling system is determined, including... The specific calculation formula is as follows: ; in, Indicates the total number of perturbed samples; This represents the convergence step number corresponding to the j-th perturbation sample; Indicates that the j-th perturbation sample is in the first position. The final state of propagation during the step; Indicates characteristic functions; The average number of convergence steps was calculated separately. and the maximum number of convergence steps and based on and The stability of the production line hypermap modeling system is determined, including... The specific calculation formula is as follows: ; in, This indicates that the sample set has been successfully converged; This indicates the number of elements in the successfully converged sample set; This represents the number of convergence steps corresponding to the s-th successfully converged sample; The specific calculation formula is as follows: .

[0030] In this embodiment, the convergence success rate is calculated. This value is used as a stability evaluation index for the production line hypergraph modeling system, reflecting its overall resilience after being subjected to external disturbances. The average number of convergence steps is calculated. This value is used as a stability evaluation index for the production line hypergraph modeling system, reflecting its typical recovery speed after being subjected to external disturbances. The maximum number of convergence steps is calculated. This is used as a stability evaluation index for the production line hypergraph modeling system, reflecting the recovery cost of the system under the most unfavorable scenario. It should be noted that this scheme, in addition to using the spectral radius of the propagation matrix M... In addition to being used as an indicator for evaluating system stability, the convergence success rate is also introduced. Average number of convergence steps and maximum convergence steps As a system stability evaluation index, through the synergistic combination of multiple indicators, it is possible to comprehensively evaluate the system stability from multiple dimensions such as the system's disturbance recovery capability, recovery speed, and recovery cost under extreme conditions, thereby improving the reliability and accuracy of the system stability evaluation results.

[0031] Furthermore, the functional units in the various embodiments of the present invention can be integrated into a processing module, or each unit can exist physically separately, or two or more units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.

[0032] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A stability analysis method for a production line hypergraph modeling system, characterized in that: Includes the following steps: Step S1: Construct the safety set of the production line hypergraph modeling system And obtain the baseline hypergraph state of the production line hypergraph modeling system. ; Step S2: Check the baseline hypergraph state By applying an external change operation sequence u, the perturbed hypergraph state is obtained. ; Step S3: Use the internal propagation mechanism to process the perturbed hypergraph state. Perform iterative updates to obtain the hypergraph state after the iteration. ,in, T represents the preset maximum number of iterations; Step S4: Calculate the potential function of the hypergraph state after iteration. and judge Does the preset system convergence condition meet? If it does, then determine... The corresponding production line hypermap modeling system enters the safety set Then proceed to step S5; if the condition is not met, continue iteratively updating the current hypergraph state until the hypergraph state corresponding to the production line hypergraph modeling system enters a safe set. ; Step S5: Enter the security set The iterative hypergraph state is mapped to a predefined parameter vector space, and the equilibrium state of the internal propagation process is obtained by solving. ; Step S6: For Perform local linearization and solve for the propagation matrix M; Step S7: Calculate the spectral radius of the propagation matrix M ,in, The specific calculation formula is as follows: ； in, This represents the magnitude of the i-th eigenvalue in the propagation matrix M; Step S8: According to The stability of the production line SuperMap modeling system is quantitatively assessed. If the production line hypergraph modeling system is locally asymptotically stable, then it is determined that the system is stable. If the system fails to meet the requirements, it is determined that the production line supermap modeling system has a strong tendency to amplify coupling or a critical instability risk.

2. The stability analysis method for a production line hypergraph modeling system according to claim 1, characterized in that: In step S1, the safety set of the production line hypergraph modeling system The specific mathematical expression is as follows: ； Where H represents any hypergraph state, This indicates the degree of constraint violation for any hyperedge e; This represents the local parameter vector associated with any hyperedge e; Represents the set of superedges; Represents the state of any hypergraph The kth key performance indicator derived; This represents the allowable range for the k-th key performance indicator; k represents the index of any indicator in the set of key performance indicators K. In step S2, the perturbed hypergraph state The specific mathematical expression is as follows: ； in, This represents the baseline hypergraph state of the production line hypergraph modeling system; u represents the external change operation sequence; This represents the external disturbance function.

3. The stability analysis method for a production line hypergraph modeling system according to claim 1, characterized in that: Step S3 specifically includes the following sub-steps: Step S31: Obtain the hypergraph state after the (t-1)th iteration. And based on this state, identify the set of active superedges participating in this iteration of propagation. ,in, ; Step S32: Obtain The nth activity superedge Corresponding vertex set ,in, The specific mathematical expression is as follows: ； Where v represents any vertex; V represents the set of superedge vertices; Represents the relationship between vertex v and active hyperedge. The membership function is used to characterize the association state between the two. Step S33: According to Constructing active hyperedges Corresponding local propagation function ,in, The specific mathematical expression is as follows: ； in, Indicates the superedge of the activity Related 3D real vector space; Step S34: Extended to an extended local propagation function defined on the parameter vector space ; Step S35: Connect each active superedge Corresponding extended local propagation function The functions are composed in iterative order to form a global propagation function in the parameter vector space. ,in, The specific mathematical expression is as follows: ； Where N represents the set of active superedges The total number of active superedges in the middle; Step S36: Propagate the global function in the parameter vector space Mapping to the hypergraph state space yields the global propagation function G corresponding to the hypergraph state space; Step S37: Apply the global propagation function G corresponding to the hypergraph state space to the hypergraph state after the (t-1)th iteration. Perform propagation iterations to obtain the hypergraph state after the t-th iteration. ,in, The specific mathematical expression is as follows: 。 4. The stability analysis method for a production line hypergraph modeling system according to claim 1, characterized in that: In step S4, the potential function of the iterated hypergraph state The specific calculation formula is as follows: ； in, This indicates the weight corresponding to the degree of constraint violation; This indicates the weight corresponding to the performance deviation. Indicates the degree of constraint violation. The specific mathematical expression is as follows: ； in, This represents the weight of the hyperedge e; Indicates the hyperedge e in the local parameter vector The degree of violation of the constraints; If in the current hypergraph state Under the condition that the production line constraints corresponding to superedge e are fully satisfied, If in the current hypergraph state When the production line constraint condition corresponding to superedge e is not met, If in the current hypergraph state When the production line constraint corresponding to the hyperedge e is a numerical inequality constraint, ,and ,in, Let e ​​represent the inequality constraint function corresponding to the hyperedge e; Indicates the degree of performance deviation. The specific mathematical expression is as follows: ； in, Represents the set of key performance indicators; This represents the weight coefficient of the k-th key performance indicator; Indicates the current hypergraph state The actual value of the kth key performance indicator; This represents the target value of the k-th key performance indicator; The Euclidean norm is used to measure the length of a set of vectors or the distance between two state vectors.

5. The stability analysis method for a production line hypergraph modeling system according to claim 1, characterized in that: In step S4, the preset system convergence conditions include: as well as .

6. The stability analysis method for a production line hypergraph modeling system according to claim 3, characterized in that: Step S5 specifically includes the following sub-steps: Step S51: Use a state mapping function to enter the safe set The iterative hypergraph state middle The vector is expanded according to a preset order to obtain an m-dimensional real vector. ,in, The specific mathematical expression is as follows: ； in, Represents the state mapping function; Step S52: Use the global propagation function in the parameter vector space right Perform propagation iterations to obtain the parameter vector state after iteration. ,in, The specific mathematical expression is as follows: ； During the propagation iteration process, when a match is found... "Conditional parameter vector state" Then the state of the parameter vector It is determined to be the equilibrium state of the internal propagation process.

7. The stability analysis method for a production line hypergraph modeling system according to claim 6, characterized in that: In step S6, for Local linearization is performed, and the specific mathematical equation is as follows: ； in, Represents the propagation matrix; Represents higher-order infinitesimal terms; This represents the deviation norm between the current parameter vector state and the equilibrium state; The specific formula for solving the propagation matrix M is as follows: 。 8. The stability analysis method for a production line hypergraph modeling system according to claim 1, characterized in that: It also includes the following steps: The convergence success rate was calculated. and based on The stability of the production line hypermap modeling system is determined, including... The specific calculation formula is as follows: ； in, Indicates the total number of perturbed samples; This represents the convergence step number corresponding to the j-th perturbation sample; Indicates that the j-th perturbation sample is in the first position. The final state of propagation during the step; Indicates characteristic functions; The average number of convergence steps was calculated separately. and the maximum number of convergence steps and based on and The stability of the production line hypermap modeling system is determined, including... The specific calculation formula is as follows: ； in, This indicates that the sample set has been successfully converged; This indicates the number of elements in the successfully converged sample set; This represents the number of convergence steps corresponding to the s-th successfully converged sample; The specific calculation formula is as follows: 。

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