An industrial chain risk monitoring method and system

Abstract

This invention provides a method and system for monitoring supply chain risks, belonging to the field of risk monitoring technology. The method includes: identifying three structural primitives and their corresponding multi-dimensional risk feature vectors in the supply chain topology network; weighting and fusing the multi-dimensional risk feature vectors to calculate the topological centroid in the risk feature space, and calibrating the topological centroid as a reference point. This invention relies on primary and secondary dual-propagation manifolds to delineate risk corridors, combined with adaptive step size quantification of node risks, to distinguish between two types of transmission paths, overcoming multiple drawbacks of traditional monitoring, and achieving dynamic quantitative risk monitoring of the entire supply chain that closely conforms to the actual transmission patterns.

Description

Technical Field

[0001] This invention relates to the field of risk monitoring technology, and in particular to a method and system for monitoring supply chain risks. Background Technology

[0002] In supply chain risk monitoring, existing methods typically rely on static network topology or time-series extrapolation models to identify and assess the propagation paths of risks between upstream and downstream nodes. In practice, these methods may have room for improvement in certain complex propagation scenarios. For example, when both dominant and local compensatory or bypass propagation paths occur simultaneously during risk propagation, existing technologies may struggle to dynamically determine the intersection area of ​​these two types of paths in the feature space, thus affecting the accuracy of defining the boundaries of feasible risk propagation intervals.

[0003] For example, in a new energy vehicle drive motor supply chain, suppose the risk event of a "shortage of rare earth permanent magnet materials" occurs upstream at "NdFeB magnet manufacturer A". Following the common transmission direction, the risk is expected to propagate along the main path: "Company A, magnet processing company B, motor stator and rotor manufacturer C, motor assembly company D, and vehicle manufacturer E". However, in actual operation, because Company C simultaneously receives supplementary supply from another magnet manufacturer F (unaffected by the shortage), the risk, after reaching Company C, may generate a compensatory diffusion path: "C, Company G (motor OEM), and vehicle manufacturer H". Existing risk monitoring methods based on fixed topology or historical propagation probabilities may struggle to simultaneously capture the risk disturbance gradient changes on the main path and the nonlinear curvature deviation on the compensatory path. This makes it difficult to determine the actual risk propagation corridor boundary formed by the intersection of the two paths in the risk feature space. This could lead to the risk monitoring system's extrapolation step size for subsequent risk evolution nodes not matching the actual propagation rhythm, ultimately affecting the reliability of the comprehensive risk situation index. Summary of the Invention

[0004] This invention provides a method and system for monitoring supply chain risks, which solves the problem of mismatch between traditional static interval characterization and the actual dynamic risk propagation situation.

[0005] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows: Firstly, a method for monitoring supply chain risks, the method comprising: Step 1: Identify the three structural primitives and their corresponding multi-dimensional risk feature vectors in the industrial chain topology network; perform weighted fusion on each multi-dimensional risk feature vector, calculate the topological centroid in the risk feature space, and mark the topological centroid as a reference point; Step 2: Calculate the first-order risk perturbation propagation gradient between the first and second structural primitives. When the magnitude of the first-order risk perturbation propagation gradient exceeds the dynamic stability threshold, construct the risk propagation main direction manifold spanned by the multi-dimensional risk feature vectors of the first and second structural primitives, starting from the reference point. Step 3: Calculate the nonlinear coupling deviation between the second-order risk cumulative curvature of the second and third structural primitives. When the nonlinear coupling deviation exceeds the curvature mismatch tolerance boundary, construct a risk propagation compensation direction manifold spanned by the multi-dimensional risk feature vectors of the second and third structural primitives, starting from the reference point. Step 4: Based on the geometric intersection region of the main risk propagation direction manifold and the risk propagation compensation direction manifold in the risk characteristic space, determine the spatial boundary envelope of the risk propagation dynamic corridor; Step 5: Within the dynamic corridor of risk propagation, calculate the local rate of change of risk intensity between adjacent topological nodes segment by segment along the topological propagation direction, and determine a set of adaptive tracking step sizes. Step 6: Perform segmented risk state extrapolation sequentially along the risk propagation dynamic corridor using a set of adaptive tracking step lengths, collect the risk diffusion intensity value and risk evolution direction angle value at the termination node of each adaptive tracking step length, and determine the topology map of the industrial chain risk propagation path and the comprehensive risk situation index.

[0006] Secondly, a supply chain risk monitoring system includes: The risk feature modeling module is used to identify three structural primitives and their corresponding multi-dimensional risk feature vectors in the industrial chain topology network; it performs weighted fusion on each multi-dimensional risk feature vector, calculates the topological centroid in the risk feature space, and marks the topological centroid as a reference point; The main propagation direction manifold construction module is used to calculate the first-order risk perturbation propagation gradient between the first and second structural primitives. When the magnitude of the first-order risk perturbation propagation gradient exceeds the dynamic stability threshold, the main risk propagation direction manifold is constructed from the reference point, which is jointly spanned by the multi-dimensional risk feature vectors of the first and second structural primitives. The compensation directional manifold construction module is used to calculate the nonlinear coupling deviation between the second-order risk cumulative curvature of the second and third structural primitives. When the nonlinear coupling deviation exceeds the curvature mismatch tolerance boundary, a risk propagation compensation directional manifold is constructed starting from the reference point, which is jointly spanned by the multi-dimensional risk feature vectors of the second and third structural primitives. The dynamic corridor boundary envelope determination module is used to determine the spatial boundary envelope of the risk propagation dynamic corridor based on the geometric intersection region of the risk propagation main direction manifold and the risk propagation compensation direction manifold in the risk feature space. The adaptive tracking step size optimization module is used to calculate the local change rate of risk intensity between adjacent topological nodes segment by segment along the topological propagation direction in the dynamic corridor of risk propagation, and determine a set of adaptive tracking step sizes. The global risk situation quantification module is used to perform segment-by-segment risk state extrapolation along the dynamic risk propagation corridor with a set of adaptive tracking step sizes, collect the risk diffusion intensity value and risk evolution direction angle value at the termination node of each adaptive tracking step size, and determine the topology map of the risk propagation path of the industrial chain and the comprehensive risk situation index.

[0007] Thirdly, a computer-readable storage medium storing a program that, when executed by a processor, implements the method.

[0008] The above-described solution of the present invention has at least the following beneficial effects: This invention abandons the single, one-sided risk indicator collection methods and undifferentiated node analysis modes of existing technologies. It aligns with the topological essence of the hierarchical coupling between upstream and downstream sectors of the industrial chain, pinpointing the core nodes carrying risk transmission within the chain. It improves the feature representation system from the source of risk, enhancing the underlying accuracy of industrial chain risk monitoring. Through hierarchical and differentiated risk feature calculation logic, it matches the linear dominant diffusion law from upstream to midstream and the nonlinear deviation transmission law from midstream to downstream, covering multi-mode risk propagation scenarios in the industrial chain. This solves the industry pain point of traditional methods failing to identify and monitor compensatory and bypass risk propagation paths. Based on vector manifold modeling and geometric envelope algorithms in the risk feature space, it dynamically fits the composite intervals of real risk propagation, locking in the effective spatial range of risk propagation. This solves the problem of mismatch between traditional static interval characterization and actual dynamic risk propagation trends, improving the accuracy of risk propagation range characterization.

[0009] By employing an adaptive segmentation and merging mechanism, this method uses a fine-grained step size to capture minute risk changes in areas of drastic risk fluctuation, while using a coarse-grained step size to optimize computational efficiency in areas of stable transmission. This approach effectively reduces algorithmic computational overhead while ensuring the accuracy of risk monitoring, balancing monitoring precision and operational efficiency. Existing technologies can only output a single risk assessment result, failing to fully reconstruct the multi-path coupled risk propagation chain, resulting in biased assessments with limited reference value. This method can fully reproduce the entire risk propagation topology of the main path and compensation path, comprehensively quantifying the overall risk situation of the industrial chain from both diffusion intensity and evolution direction dimensions. The assessment results closely reflect the actual operating status of the industrial chain, providing comprehensive decision-making basis for industrial chain risk early warning, risk tracing, hierarchical control, and supply chain emergency regulation, effectively improving the intelligent level of industrial chain risk security management. Attached Figure Description

[0010] Figure 1This is a flowchart illustrating a supply chain risk monitoring method provided by an embodiment of the present invention.

[0011] Figure 2 This is a schematic diagram of a supply chain risk monitoring system provided by an embodiment of the present invention. Detailed Implementation

[0012] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0013] like Figure 1 As shown in the figure, an embodiment of the present invention proposes a supply chain risk monitoring method, the method comprising the following steps: Step 1: Identify the three structural primitives and their corresponding multi-dimensional risk feature vectors in the industrial chain topology network; perform weighted fusion on each multi-dimensional risk feature vector, calculate the topological centroid in the risk feature space, and mark the topological centroid as a reference point; Step 2: Calculate the first-order risk perturbation propagation gradient between the first and second structural primitives. When the magnitude of the first-order risk perturbation propagation gradient exceeds the dynamic stability threshold, construct the risk propagation main direction manifold spanned by the multi-dimensional risk feature vectors of the first and second structural primitives, starting from the reference point. Step 3: Calculate the nonlinear coupling deviation between the second-order risk cumulative curvature of the second and third structural primitives. When the nonlinear coupling deviation exceeds the curvature mismatch tolerance boundary, construct a risk propagation compensation direction manifold spanned by the multi-dimensional risk feature vectors of the second and third structural primitives, starting from the reference point. Step 4: Based on the geometric intersection region of the main risk propagation direction manifold and the risk propagation compensation direction manifold in the risk characteristic space, determine the spatial boundary envelope of the risk propagation dynamic corridor; Step 5: Within the dynamic corridor of risk propagation, calculate the local rate of change of risk intensity between adjacent topological nodes segment by segment along the topological propagation direction, and determine a set of adaptive tracking step sizes. Step 6: Perform segmented risk state extrapolation sequentially along the risk propagation dynamic corridor using a set of adaptive tracking step lengths, collect the risk diffusion intensity value and risk evolution direction angle value at the termination node of each adaptive tracking step length, and determine the topology map of the industrial chain risk propagation path and the comprehensive risk situation index.

[0014] In this embodiment of the invention, core risk nodes are screened based on the industrial chain topology, and a complete multi-dimensional risk feature system is built to improve the accuracy of risk monitoring from the fundamental level. A hierarchical differentiated computational logic is adopted to adapt to both linear and nonlinear risk transmission modes in the industrial chain, avoiding the omission of detour and compensation risk paths. Vector manifold and geometric envelope algorithms are used to dynamically delineate risk propagation intervals, overcoming the problem of inconsistency between traditional static intervals and the actual propagation situation, thus characterizing the risk propagation range. Simultaneously, an adaptive step-size adjustment mechanism is introduced, using fine step-sizes in risk fluctuation areas to ensure identification accuracy and coarse step-sizes in stable sections to reduce computation, balancing monitoring effectiveness and algorithm efficiency. Unlike existing technologies that can only output a single, partial evaluation value and cannot reconstruct the multi-path coupled propagation process, this method reconstructs the topological structure of the main propagation path and the compensation propagation path, and comprehensively quantifies the overall risk by combining two indicators: risk diffusion intensity and evolutionary offset direction. The evaluation results closely match the actual operation of the industrial chain, improving the intelligence level of industrial chain risk management.

[0015] In a preferred embodiment of the present invention, step 1 includes: Step 100a: Traverse all nodes in the industry chain topology network, and classify each node into the upstream supply layer node set, the midstream manufacturing layer node set, and the downstream distribution layer node set according to the industry chain level to which the node belongs. Specifically, this includes: A pre-constructed supply chain topology network is established, with participating enterprises, production units, and distribution points as topology nodes, and material transportation relationships, component matching relationships, production assembly dependencies, and market supply and demand connections as topology edges, forming a complete directed relational topology structure. A comprehensive traversal of this supply chain topology network is performed, systematically reading the basic information of each topology node, including its node attributes, business functions, upstream and downstream partners, production stage, and market connection attributes. Based on the functional positioning of each topology node in the supply chain value transmission and production chain, all topology nodes are systematically divided into three mutually exclusive and fully covering node sets: the upstream supply layer node set, the midstream manufacturing layer node set, and the downstream distribution layer node set.

[0016] The upstream supply layer node set specifically includes supply-type topology nodes that provide basic raw materials, core components, and primary supporting parts for core products in the industrial chain. These nodes are at the forefront of the industrial chain and undertake the function of supplying basic materials. The midstream manufacturing layer node set specifically includes production-type topology nodes that process, assemble, shape, and integrate upstream input materials and components. These nodes have material integration and product processing and manufacturing capabilities and serve as the intermediate transmission hub of the industrial chain. The downstream distribution layer node set specifically includes circulation-type topology nodes that connect with the end consumer market, complete finished product delivery, order fulfillment, and market demand response. These nodes are directly related to fluctuations in the end market. After traversal and classification, all topology nodes uniquely belong to a single layer set.

[0017] Step 101a: In the upstream supply layer node set, select the node with the highest degree centrality and a primary bill of materials dependency relationship with the core product of the industrial chain as the first structural primitive; in the midstream manufacturing layer node set, select the node with the highest betweenness centrality that undertakes the function of assembling multi-source components as the second structural primitive; in the downstream distribution layer node set, select the node with the highest degree centrality that connects to the terminal market demand convergence port as the third structural primitive, specifically including: Based on the node set division of the upstream supply layer, midstream manufacturing layer, and downstream distribution layer completed in step 100a, and considering the completely different risk transmission mechanisms of the three layers of the industry chain, a differentiated topological centrality index combined with business function constraints is used to select core nodes as structural primitives layer by layer. The upstream, midstream, and downstream of the industry chain have completely different functional attributes in the risk propagation chain. The upstream is the source of risk and its core characteristic is the outward multi-path radiation and diffusion of single-point risks; the midstream is the central transfer point of risk and its core characteristic is the convergence of multiple upstream risks and their diversion and transmission to the downstream, serving as an essential hub for the cross-layer propagation of risks across the entire network; the downstream is the terminal feedback point of risk and its core characteristic is the absorption of risks across the entire network, the perception of terminal market fluctuations, and the reverse back-to-upward transmission. Based on the above hierarchical differences, extreme value screening is performed on the nodes of the three layers according to degree centrality, betweenness centrality, and proximity centrality, respectively, to ensure that the finally selected structural primitives can represent the dominant risk propagation characteristics of the corresponding level.

[0018] The first structural primitive is selected from the upstream supply layer node set. The core risk behavior at the upstream level is source-borne risk. Once a single core supply node experiences an anomaly, it will directly affect all its supporting downstream production nodes. The breadth of direct connections between nodes determines their risk radiation capacity. Degree centrality is used to quantify the scale of direct adjacency of nodes in the topology network, which can characterize the material supply coverage and risk diffusion amplitude of upstream nodes. First, upstream supply layer nodes are screened under business constraints, retaining candidate nodes that have a first-level bill of materials dependency relationship with the core products of the industrial chain. These nodes are the direct material supply source of the core products and are the initial carriers of upstream risk propagation. The total number of nodes in the industrial chain topology network is set to be... For any upstream candidate node The formula for calculating node degree centrality is as follows: ; In the formula, For elements of the topological adjacency matrix, if node With nodes The value is 1 if there is a direct topological edge connection, and 0 if there is no direct connection. For nodes The degree centrality of a node is numerically equivalent to the total number of its direct neighboring nodes. A higher degree centrality indicates a larger number of directly connected nodes in the upstream supply chain, resulting in a stronger ability to spread risk sources and a wider range of disturbances. By traversing all upstream candidate nodes, the unique node with the highest degree centrality is selected as the first structural primitive to characterize the source-diversifying risk characteristics of the upstream supply layer.

[0019] The midstream manufacturing layer bears the core functions of multi-source component aggregation, integration and assembly, and cross-layer risk transfer. It is a key hub connecting upstream supply and downstream distribution. The vast majority of cross-layer risk propagation paths in the industrial chain must be transferred, diverted, and retransmitted through core midstream nodes. The node's ability to control the path hub determines the overall network risk propagation efficiency. Betweenness centrality is used to quantify the degree of control a node has over the shortest risk propagation path in the entire network, and can identify hub nodes that undertake core transfer and transmission functions. First, midstream manufacturing layer nodes are screened based on business constraints, retaining candidate nodes with multi-source component aggregation and assembly functions. These nodes have the ability to integrate and produce multiple materials and are the core carriers of midstream risk aggregation and secondary diffusion. The formula for calculating node betweenness centrality is as follows: ; In the formula, For nodes To the node The total number of all shortest topological paths; For nodes To the node The shortest path passes through the nodes The number of paths; For nodes The betweenness centrality of a midstream node is considered. A higher betweenness centrality value indicates a more crucial pivotal role for the midstream node in the overall risk transmission chain, and a more significant effect on controlling, diverting, and amplifying risk propagation across levels. By traversing all candidate midstream nodes, the unique node with the highest betweenness centrality value is selected as the second structural primitive to characterize the pivotal transformation risk characteristics of the midstream manufacturing layer.

[0020] The downstream distribution layer directly connects to the convergence port of end-market demand. It is both the final point of entry for risk propagation in the industry chain and the starting point for the reverse transmission of market risk and fluctuations in end-market demand. The network-wide accessibility and global linkage capability of nodes are core characteristics of downstream risk propagation. Proximity centrality is used to quantify the average shortest propagation distance from a node to all topological nodes in the network, characterizing the node's global accessibility and risk reverse transmission capability. First, downstream distribution layer nodes are screened based on business constraints, retaining candidate nodes connected to the convergence port of end-market demand. These nodes directly perceive end-market fluctuations and are the core carriers of downstream risk feedback and reverse transmission. The formula for calculating node proximity centrality is as follows: ; In the formula, This represents the total number of nodes in the network. For nodes To the node The shortest topological distance; For nodes The closer centrality of a node is considered. A higher close centrality value indicates a shorter average path and faster transmission speed from the downstream node to all nodes in the entire industry chain, resulting in stronger sensitivity to global risk situations and greater reverse tracing and propagation capabilities. By traversing all downstream candidate nodes, the unique node with the highest close centrality value is selected as the third structural primitive to characterize the terminal feedback and rapid accessibility risk characteristics of the downstream distribution layer.

[0021] Step 102a: For the first, second, and third structural primitives, collect the node's own operational status deviation, the upstream and downstream supply-demand gap ratio associated with the node, and the historical spatiotemporal propagation trajectory records of risk events within the local topological neighborhood of the node as multi-dimensional risk feature vectors for the corresponding structural primitives, specifically including: For the first, second, and third structural primitives, data collection was conducted using a uniform 30-day continuous time-series statistical period. Three types of quantifiable risk characteristic indicators were collected simultaneously to construct a multi-dimensional risk feature vector that is dimensionally unified, time-series aligned, and spatially computable. Let the multi-dimensional risk feature vector of any structural primitive be denoted as... ,in For operational status deviation, For the supply-demand gap ratio, For standardized spatiotemporal trajectory feature quantities.

[0022] Three core operational parameters—capacity utilization rate, order fulfillment rate, and equipment operating efficiency—are selected. The absolute deviations of the actual parameters from the benchmark stable parameters are calculated for each parameter. Then, min-max normalization is used to fuse these deviations to obtain the dimensionless operational state deviation. First, the deviation of a single type of operational parameter is defined, i.e. ,in This represents the actual operational parameter values ​​corresponding to the nodes within the current time series period. This represents the baseline operating parameter values ​​for the node within its historical stable operating range. Multiple deviations are normalized using a min-max method, and the final result is the operational status deviation. When... When the condition is met, the value of this item is 0; otherwise, it is calculated according to the original formula. That is: ; In the formula: This represents the number of operational parameter categories, with a value of 3, corresponding to capacity utilization, order fulfillment rate, and equipment operating efficiency, respectively. It is the minimum value among the three types of operational parameter deviations; It is the maximum value among the three types of operational parameter deviations; The deviation from the operational status is represented by a higher value, indicating a higher degree of operational abnormality and a higher level of inherent risk for the node.

[0023] The upstream and downstream supply and demand data of nodes within the same time period are statistically analyzed. The degree of supply and demand imbalance in the link is quantified by the ratio of the supply and demand difference to the total supply. The calculation formula is as follows: ; In the formula This represents the total effective downstream order demand corresponding to the node within the current time series. This represents the maximum total supply of upstream materials corresponding to the node within the current time series. This represents the supply-demand gap ratio. A value greater than 0 indicates that demand exceeds supply, and the node faces the risk of insufficient material supply, supply disruptions, and work stoppages. A value less than 0 indicates that supply exceeds demand, and the node carries the risk of overcapacity, unsold finished products, and inventory backlog.

[0024] Using structural primitives as central nodes, risk event samples with a fixed topological hop count neighborhood and a fixed historical duration are extracted. The historical duration is uniformly fixed at 12 months, and the topological neighborhood is a fixed set of first-order neighborhood nodes centered on the primitive node. The frequency of occurrence, average duration, and average number of affected nodes of risk events within this fixed spatiotemporal range are statistically analyzed. After normalization of these three statistical measures, they are weighted and fused to obtain a single spatiotemporal feature quantification value. The calculation formula is as follows: ; In the formula This represents the normalized frequency of risk events. This represents the normalized average duration of risk events. This represents the average number of nodes affected by a risk event after normalization. , , To ensure fixed normalized weight coefficients, the total weights are fixed at 1, and the system is unified. =0.4、 =0.3、 =0.3; This is a historical spatiotemporal propagation trajectory feature quantity. This feature quantity is obtained by weighted fusion of the frequency of risk events occurring, duration of impact, and affected node range within a fixed historical period of 12 months in the local first-order topological neighborhood. It can quantitatively reflect the activity level, propagation and diffusion capabilities, and inherent structural vulnerability level of past risk outbreaks in the local topological region of that node. Through the above complete calculation logic, the first structural primitive feature vector with unified dimensions, consistent parameter caliber, and unified value standards is obtained. Second structural primitive eigenvector Third structural primitive eigenvector .

[0025] Step 100b: Obtain the node-level weight coefficients of the first, second, and third structural primitives in the industry chain topology network. The node-level weight coefficients are determined based on the inverse ratio of the topological distance between the corresponding structural primitive's industry chain level and the industry chain's end-consumer layer. Specifically, this includes: After constructing the multi-dimensional risk feature vectors of three sets of structural primitives, to differentiate the weights of the varying impacts of upstream, midstream, and downstream nodes on the overall risk profile of the industry chain, a topological distance inverse ratio mechanism is used to calculate the node level weight coefficients corresponding to each primitive, based on the shortest topological distance between the industry chain level where the structural primitive resides and the end-consumer layer of the industry chain. Industry chain risk transmission exhibits a natural hierarchical attenuation characteristic; the closer a node is to the end-consumer layer, the more direct the impact of risk fluctuations on the overall risk profile of the end-consumer industry chain, and the higher its weight should be. Conversely, the farther a node is from the end-consumer layer, the weaker the impact of risk on the end-consumer profile after multi-level transmission attenuation, and the lower its weight should be. This mechanism avoids the distortion of the risk benchmark caused by equal weighting. The shortest topological distance is defined as the minimum number of industry chain level jumps required for the corresponding structural primitive to propagate to the end-consumer layer. Let the shortest topological distances from the first, second, and third structural primitives to the end-consumer layer be respectively... First, the initial weight coefficients of each primitive are calculated based on the inverse relationship of topological distance. The formula for calculating the initial weights is as follows: ; In the formula, the subscript The values ​​are 1, 2, and 3, which correspond to the first structural primitive, the second structural primitive, and the third structural primitive, respectively. For the first The shortest topological distance at each level corresponding to a structural primitive; The initial inverse weights are unnormalized. The larger the topological distance, the smaller the initial weight value, which conforms to the law of risk transmission and attenuation in the industrial chain.

[0026] To ensure that multiple weight coefficients can participate uniformly in vector fusion calculations and that the weights as a whole are subject to normalization constraints, global normalization is applied to the three initial weights to obtain the standardized node-level weight coefficients used for risk feature correction. The normalization calculation formula is as follows: ; In the formula, For the first The final normalized hierarchical weight coefficients corresponding to each structural primitive, and the sum of the three sets of weight coefficients are always equal to 1.

[0027] Step 101b involves multiplying the multi-dimensional risk feature vector of each structural primitive by its corresponding node-level weight coefficient to obtain a weighted risk feature vector, specifically including: Based on the three sets of original multi-dimensional risk feature vectors obtained in step 102a and the corresponding normalized hierarchical weight coefficients obtained in step 100b, a scalar multiplication and weighted operation of the vectors is performed to achieve differentiated correction of risk features at different levels, weaken the interference of weakly correlated risks at the far level, strengthen the strongly correlated risk features at the near end, and make the risk vector conform to the distribution of the real transmission influence of the industrial chain.

[0028] The original multi-dimensional risk feature vectors are unified into a three-dimensional structure, sequentially containing operational status deviation, supply-demand gap ratio, and historical spatiotemporal propagation trajectory features collected over a 30-day time series period. The three sets of primitive vector dimensions are perfectly aligned. The weighted correction calculation formula is as follows: ; In the formula, For the first The original multidimensional risk feature vector of each structural primitive; These are the corresponding normalized hierarchical weight coefficients; This is the standardized risk feature vector after weighted correction. This operation is a scalar multiplication of the vector dimension by dimension, meaning that each dimensional feature component within the original vector is independently multiplied by the corresponding hierarchical weight coefficient, preserving the dimensional structure and relative distribution of the original risk features, and only completing the differential correction of hierarchical influence.

[0029] Through the above calculations, the weighted risk feature vectors of the first structural primitives are obtained respectively. Second structural primitive weighted risk feature vector Third structural primitive weighted risk feature vector The three sets of weighted vectors are uniformly mapped to the same high-dimensional risk feature space, which has the computational basis for global vector superposition and geometric solution.

[0030] Step 102b involves superimposing the three weighted risk feature vectors in the risk feature space, calculating the geometric center of the resulting vector, and defining the geometric center as the topological centroid. The coordinate vector of the topological centroid in the risk feature space is then used as a reference point. Specifically, this includes: By performing spatial vector superposition on the three sets of weighted risk feature vectors, a global resultant vector is obtained: ; Further, the geometric center of the composite vector is determined, which is the topological centroid of the risk feature space. The coordinates of each dimension of the centroid are the arithmetic mean of the corresponding dimensional components of the composite vector. Let the total dimension of the feature vector be... (In this embodiment, the multi-dimensional risk feature vector is fixedly composed of three dimensions: operational status deviation, supply-demand gap ratio, and spatiotemporal propagation trajectory characteristics. Therefore...) =3), topological centroid vector The formulas for calculating the components of each dimension are as follows: ; in The first of the topological centroid coordinate vectors 1D component; the high-dimensional coordinate vector of the topological centroid obtained by solving. The coordinate vector, which is uniquely designated as the global reference point in the risk feature space, integrates the quantitative risk characteristics and hierarchical topological weight differences of the three core structural primitives, and depicts the overall benchmark risk steady-state position of the industrial chain in the current time series. It can serve as a zero-deviation reference benchmark in the risk feature space.

[0031] This embodiment improves monitoring targeting by screening core transmission elements of industry chain risks through hierarchical classification of network nodes and multi-level centrality indicators. It changes the traditional random and indiscriminate node analysis method. It constructs a multi-dimensional risk feature vector that includes three dimensions: endogenous operation, supply and demand coupling, and spatiotemporal propagation, to solve the defects of single indicator representation and monitoring distortion. It sets hierarchical weights based on the inverse rule of topological distance to weight and fuse the feature vectors, distinguishing the transmission influence of upstream and downstream nodes, eliminating the benchmark deviation caused by equal superposition, and making the topological weighted centroid fit the real transmission law. It solves the global reference point through standardized vector operation, which is uniformly used as the calculation benchmark for gradient, curvature, manifold modeling, and adaptive step size extrapolation, ensuring the logical consistency of the entire risk extrapolation process.

[0032] In a preferred embodiment of the present invention, step 2 includes: Step 200: Within a continuous time window, perform time-series differencing operations on the multi-dimensional risk feature vectors of the first structural primitive and the second structural primitive, respectively, to obtain the first risk feature difference sequence and the second risk feature difference sequence, specifically including: Based on the three-dimensional multi-dimensional risk feature vectors of the first and second structural primitives that have been constructed, time-series difference operations are performed using a continuous time-series window of fixed duration to extract the risk time-series fluctuation increments from the upstream supply layer to the midstream manufacturing layer nodes, eliminating static feature baseline interference and highlighting the dynamic disturbance change patterns of risk. A sliding continuous time-series window with a uniform duration of 30 days is adopted, and a fixed sampling frequency of once per day is set, that is, the multi-dimensional risk feature vectors of the structural primitives are sampled and collected once every 24 hours. The multi-dimensional risk feature vectors of the first and second structural primitives are collected hourly according to the fixed sampling frequency of once per day, forming two sets of time-series feature vector sequences.

[0033] For continuous feature sequences within a time window, a dimension-wise temporal differencing calculation is performed to characterize the dynamic changes in risk characteristics between adjacent time points. The temporal differencing calculation formula is as follows: ; In the formula, This represents the multi-dimensional risk feature vector at the current sampling time. This is the multi-dimensional risk feature vector from the previous adjacent sampling time. This is the temporal difference vector corresponding to the current moment. This difference vector independently calculates the numerical differences between adjacent daily sampling moments for three dimensions: operational status deviation, supply-demand gap ratio, and spatiotemporal propagation trajectory characteristics. The absolute value of the difference in each dimension accurately corresponds to the instantaneous volatility of the corresponding dimension's risk characteristics. The positive or negative sign of the difference corresponds to the temporal evolution direction of the corresponding dimension's risk characteristics: a positive value indicates that the risk characteristic of that dimension has increased compared to the previous moment, and the risk situation has intensified; a negative value indicates that the risk characteristic of that dimension has decreased compared to the previous moment, and the risk situation has eased. This achieves a precise quantitative representation of the dynamic fluctuation degree and evolution trend of multi-dimensional risks at a single moment, effectively compensating for the deficiency of static features, which can only display instantaneous risk states and cannot capture dynamic evolution patterns.

[0034] The feature vectors within the full-time window of the first structural primitive are subjected to time-series difference operations, and arranged in temporal order to generate the first risk feature difference sequence. The same time-series difference operations are performed on the feature vectors within the full-time window of the second structural primitive, and arranged in corresponding temporal order to generate the second risk feature difference sequence. The two sets of difference sequences are aligned in time length and have a unified dimensional structure, fully preserving the temporal dynamic perturbation information of risks from upstream to midstream nodes.

[0035] Step 201: Perform time-series cross-correlation analysis on the first risk feature difference sequence and the second risk feature difference sequence, extract the maximum cross-correlation coefficient and the corresponding lag step size, use the maximum cross-correlation coefficient as the magnitude of the first-order risk perturbation propagation gradient, and use the lag step size as the propagation delay of the first-order risk perturbation propagation gradient. Specifically, this includes: For the first risk feature difference sequence and the second risk feature difference sequence obtained in step 200, a global time series cross-correlation analysis is carried out to quantify the linear transmission correlation strength and transmission lag characteristics of the upstream first structural element risk disturbance to the midstream second structural element, thereby solving the first-order risk disturbance propagation gradient.

[0036] Since both sets of difference sequences are three-dimensional vector sequences, the time-series cross-correlation calculation is performed as follows: for each dimension component of the difference vector... ( =1, 2, 3), calculate the scalar cross-correlation for each dimension, and then take the arithmetic mean of the three dimensions as the final cross-correlation coefficient. The formula for calculating the single-dimensional cross-correlation is as follows: ; In the formula, For the first difference sequence Dimensional Moment The value, For the second difference sequence Dimensional Moment The value, Let covariance be the variance of the two scalar sequences. Let be the variance of the scalar sequence. The final cross-correlation coefficient is: .

[0037] Traverse all legal lag steps from 1 to 30 days (Due to a time window length of 30 days and a sampling frequency of once per day), the corresponding final cross-correlation coefficients are calculated by substituting each value into the formula, and the maximum cross-correlation coefficient and its corresponding optimal lag step are obtained. The maximum cross-correlation coefficient characterizes the linear correlation strength of upstream supply-side risk disturbances propagating to the midstream manufacturing layer. The closer the coefficient is to 1, the more significant the transmission effect of upstream risk disturbances driving synchronous changes in midstream risk. The optimal lag step is used to characterize the inherent time delay of this risk transmission, quantifying how many sampling periods are needed for the upstream risk anomaly to propagate to the midstream node. The maximum cross-correlation coefficient is directly defined as the amplitude of the first-order risk disturbance propagation gradient. The larger the value, the stronger the linear risk disturbance transmission correlation from upstream to midstream and the more significant the risk-dominant diffusion effect. The optimal lag step is defined as the propagation delay of the first-order risk disturbance propagation gradient, used to characterize the time lag characteristics of upstream risk disturbance propagation to midstream nodes, fully quantifying the first-order linear risk propagation law from upstream to midstream.

[0038] Step 202: Compare the magnitude of the first-order risk perturbation propagation gradient with the dynamic stability threshold. When the magnitude of the first-order risk perturbation propagation gradient is greater than the dynamic stability threshold, using the reference point as the starting point for manifold construction, the multi-dimensional risk feature vector of the first structural primitive is used as the first directional basis, and the multi-dimensional risk feature vector of the second structural primitive is used as the second directional basis. The first and second directional bases span the risk feature space to form the main direction manifold for risk propagation. Specifically, this includes: The effectiveness of the first-order risk disturbance propagation gradient amplitude is determined by using a dynamic stability threshold, identifying the dominant risk propagation pathway from upstream to midstream of the industrial chain, and constructing a main-direction risk propagation manifold in the risk feature space. The dynamic stability threshold is determined through historical data calculation. Specifically, under 12 consecutive months of stable operation of the industrial chain, the amplitude of the first-order risk disturbance propagation gradient corresponding to all time windows is statistically analyzed, and the 90th quantile of this stable sample set is extracted as the dynamic stability threshold. The historical stable operation is defined as follows: during this period, the monthly fluctuation of core output indicators of the industrial chain (such as capacity utilization rate and order fulfillment rate) does not exceed ±1 standard deviation of its historical mean, and there are no records of major risk events (such as factory shutdowns or large-scale supply disruptions). Assuming the calculated threshold value is 0.6, it can effectively filter out small, normal daily fluctuations in the industrial chain, retaining only risk disturbances with substantial transmission capabilities, and distinguishing between normal small fluctuations and substantial risk transmission disturbances.

[0039] The magnitude of the first-order risk disturbance propagation gradient obtained in step 201 is compared with the dynamic stability threshold of 0.6. Only when the magnitude of the first-order risk disturbance propagation gradient is greater than 0.6 is it determined that a substantial and high-intensity linear risk disturbance has occurred from the upstream supply layer to the midstream manufacturing layer, and the main risk propagation path is activated.

[0040] When the criteria for activation of the main pathway are met, the global reference point of the risk feature space determined by the solution is used as the unique and fixed origin of the manifold construction, thereby ensuring the consistency of the benchmark for all manifold modeling. The first structural primitive multi-dimensional risk feature vector, representing the upstream source diffusion risk characteristics, is selected as the first directional basis to anchor the initial propagation direction and feature base of upstream risk disturbances in the industrial chain. The second structural primitive multi-dimensional risk feature vector, representing the midstream hub transfer risk characteristics, is selected as the second directional basis to anchor the propagation direction and feature base of midstream risk acceptance and evolution in the industrial chain. Within a unified three-dimensional risk feature space composed of operational deviation, supply-demand gap ratio, and spatiotemporal propagation trajectory characteristics, a unique two-dimensional affine manifold is formed by extending the global reference point as the origin and relying on the two sets of linearly independent directional bases through a global linear combination. This manifold strictly conforms to the propagation law of linear risk disturbances from the upstream supply layer to the midstream manufacturing layer, fully encompassing the upstream-to-midstream risk evolution path and feature change range under different disturbance intensities and different transmission lag periods, and can cover the explicit and dominant risk transmission behavior of the industrial chain. Ultimately, this two-dimensional affine manifold is uniquely defined as the main direction manifold for risk propagation, used to quantitatively characterize the spatial propagation coverage, characteristic evolution law, and inherent propagation extension direction of the core dominant risks in the industrial chain.

[0041] This embodiment extracts the propagation gradient and delay characteristics of first-order linear risk disturbances from upstream to midstream through a quantitative approach combining time-series differencing and time-series cross-correlation analysis, enabling the quantitative identification and activation determination of dominant risk propagation. By eliminating static baseline interference through standardized time-series differencing and accurately characterizing the linear transmission correlation strength through cross-correlation coefficients, it can capture the dominant risk diffusion behavior from upstream to midstream of the industrial chain, achieving accurate identification of risk propagation from the linear transmission dimension.

[0042] In a preferred embodiment of the present invention, step 3 includes: Step 300 involves estimating the time-series second derivative of the multi-dimensional risk feature vectors of the second and third structural primitives to obtain the second-order risk cumulative curvature of the second and third structural primitives, specifically including: Risk propagation from upstream to midstream is mainly driven by first-order linear disturbances, while risk propagation from midstream to downstream is affected by multi-source component adaptation, market demand fluctuations, and multi-level capacity coupling, exhibiting significant nonlinear cumulative evolution characteristics. This step uses time-series second derivative estimation to quantify the nonlinear cumulative change law of risk at midstream and downstream nodes, and obtains the second-order risk accumulation curvature.

[0043] Based on the multi-dimensional risk feature time series of the second and third structural primitives within a continuous time window obtained at a fixed sampling frequency of once per day, time series second derivative estimation is performed dimension by dimension. First, the rate of risk change is obtained through first-order time series differencing. Then, the degree of change of the rate of change is solved by differentiating the rate of change sequence again, which is the second-order time series derivative, used to characterize the cumulative accelerated evolution characteristics of risk, and is defined as the second-order risk cumulative curvature.

[0044] The formula for calculating the second-order risk cumulative curvature is as follows: First, calculate the temporal second-order difference of the three-dimensional vector: ; Then, the magnitude of this difference vector is taken as the scalar value of the second-order risk cumulative curvature, that is: ; In the formula, It is a three-dimensional temporal second-order difference vector. Let d be the dd-th dimension component of this vector. This represents the final second-order risk cumulative curvature scalar value. This scalar value quantifies the overall acceleration / deceleration of the risk change rate at midstream or downstream nodes by integrating the nonlinear cumulative change amplitude of three-dimensional risk characteristics. A larger value indicates a more significant nonlinear cumulative effect of risk, while a smaller value indicates a smoother risk evolution. The second-order risk cumulative curvature scalar sequences for the second and third structural primitives are obtained through calculation.

[0045] Step 301: Input the second-order risk cumulative curvature of the second and third structural primitives into a pre-constructed nonlinear coupling mapping function to calculate the nonlinear coupling deviation; wherein, the nonlinear coupling mapping function is used to characterize the difference in asymmetric risk transmission elasticity between the midstream manufacturing layer and the downstream distribution layer, specifically including: A pre-constructed nonlinear coupling mapping function, specifically adapted to the risk transmission characteristics of the midstream manufacturing layer and the downstream distribution layer, is used to characterize the inherent asymmetric risk transmission elasticity differences between the two levels. This addresses the technical shortcomings of traditional linear correlation models, which cannot fit the differentiated nonlinear risk evolution patterns of midstream convergence and amplification, and downstream sensitive feedback. Midstream manufacturing layer risks are characterized by multi-source convergence, rigid capacity constraints, and cumulative risk amplification, while downstream distribution layer risks are characterized by market volatility sensitivity, reverse demand tracing, and rapid volatility decay. The mismatch in risk evolution elasticity between the two levels and the nonlinear transmission relationship make accurate quantification impossible using linear correlation models. This function uses the second-order risk accumulation curvature of the second structural primitive and the second-order risk accumulation curvature of the third structural primitive as input variables. Parameter fitting and training are completed based on 12 consecutive months of historical stable and historical risk conditions across the industry chain, forming a stable and reproducible nonlinear mapping relationship. The specific calculation formula for the nonlinear coupling mapping function is as follows: ; In the formula, For pre-trained nonlinear coupling mapping functions; The second-order risk cumulative curvature scalar value of the second structural primitive (obtained from step 300); To fit the second-order curvature to the third structural primitive theory obtained through nonlinear mapping; The first-order linear coupling coefficients, The two coefficients are second-order nonlinear correction coefficients, both of which are obtained by training and solidifying from the entire historical sample dataset. Specifically, they are obtained by fitting and training a complete set of historical stable and risky operating conditions samples from the entire industrial chain over 12 consecutive months using the least squares method. Specifically, paired samples of midstream and downstream second-order risk cumulative curvature are collected in batches from historical time series to construct a historical sample dataset. Then, the downstream real second-order risk cumulative curvature is used as the fitting target value, and the midstream second-order risk cumulative curvature is used as the input feature value. The optimal parameter combination is iteratively solved based on the least squares loss function. The parameters are continuously iterated and updated to minimize the fitting loss, and a convergence threshold is set. When the fluctuation value of the loss function is less than the threshold and the parameter values ​​are basically stable after 5 consecutive iterations, the iteration is considered to have converged and the operation is terminated. The globally optimal first-order linear coupling coefficient and second-order nonlinear correction coefficient are then fixed, and their values ​​are assumed to be as follows: It is used to simultaneously fit the linear transmission law and nonlinear distortion law of two levels of risk.

[0046] After the mapping and fitting are completed, the nonlinear coupling deviation is obtained by calculating the difference between the real curvature and the theoretically fitted curvature. ; In the formula, This represents the real-time nonlinear coupling deviation. The real second-order risk cumulative curvature obtained by real-time acquisition and calculation of the third structural primitive; The second-order curvature is fitted to the downstream theoretical value obtained through nonlinear coupling mapping function. The smaller the absolute value of the deviation, the higher the match between the nonlinear evolution law of midstream and downstream risks, and the stable and undistorted conventional risk transmission path from midstream to downstream of the industrial chain. The larger the absolute value of the deviation, the more serious the mismatch between the nonlinear evolution law of the two levels of risks, the imbalance of transmission elasticity, the failure of conventional forward transmission path, and the high likelihood of unconventional risk propagation branches such as compensatory detours and reverse transmission in the industrial chain.

[0047] Step 302: Compare the nonlinear coupling deviation with the curvature mismatch tolerance boundary. When the absolute value of the nonlinear coupling deviation is greater than the curvature mismatch tolerance boundary, take the reference point as the starting point for manifold construction, use the multidimensional risk feature vector of the second structural element as the third directional basis, and the multidimensional risk feature vector of the third structural element as the fourth directional basis. A risk propagation compensation directional manifold is spanned in the risk feature space through the third and fourth directional bases. The curvature mismatch tolerance boundary is determined based on the maximum value of the nonlinear coupling deviation of the second-order risk cumulative curvature between the second and third structural elements during the historical stable operation period, specifically including: A preset curvature mismatch tolerance boundary is determined through historical data calculation. Specifically, it involves selecting 12 consecutive months of historical stable operating sequence data for the second and third structural primitives, calculating the corresponding nonlinear coupling deviation at each time step, and statistically analyzing the maximum absolute value of the deviation under all stable operating conditions. This maximum absolute value is then fixed as the curvature mismatch tolerance boundary. The definition of the historical stable operating conditions is consistent with that in step 202. Assuming the calculated boundary value is 0.3, representing the maximum allowable nonlinear coupling mismatch range under normal steady-state operation of the supply chain, it is used to distinguish between normal nonlinear fluctuations and abnormal risk mismatch transmission.

[0048] The real-time nonlinear coupling deviation calculated in step 301 is compared with the curvature mismatch tolerance boundary with a value of 0.3. When the absolute value of the nonlinear coupling deviation is greater than 0.3, it is determined that the conventional linear transmission path from the midstream to the downstream has failed, and the industrial chain activates compensatory and bypass nonlinear risk propagation paths.

[0049] When the conditions for activation of the compensation pathway are met, the modeling benchmark consistent with the main direction manifold construction is continued. The globally reference point of the risk feature space with unified calibration is used as the origin of the fixed manifold construction. The second structural primitive multidimensional risk feature vector, which represents the midstream hub transfer risk and has nonlinear cumulative amplification characteristics, is selected as the third directional basis to anchor the output basis and propagation starting direction of the midstream abnormal mismatch risk. The third structural primitive multidimensional risk feature vector, which represents the downstream terminal distribution risk and has market-sensitive feedback characteristics, is selected as the fourth directional basis to anchor the evolution termination direction of the downstream risk acceptance shift.

[0050] Within a unified three-dimensional risk characteristic space comprised of operational deviation, supply-demand gap ratio, and spatiotemporal propagation trajectory characteristics, and relying on two sets of linearly independent directional bases, nonlinear spatial extension modeling is conducted for nonlinear mismatch conditions in the midstream and downstream sectors. This results in a dedicated two-dimensional nonlinear manifold that adapts to the risk bypass and compensation transmission patterns. This manifold differs from conventional linear propagation paths, fully covering the propagation paths, characteristic variation ranges, and dynamic evolution intervals of various compensatory, bypass, and nonlinear offset risks arising from conventional transmission failures from the midstream to the downstream, accommodating asymmetric risk transmission behaviors that linear models cannot characterize. Ultimately, this nonlinear manifold is uniquely defined as a risk propagation compensation directional manifold, used to quantitatively characterize the spatial coverage, distortion propagation patterns, and offset evolution directions of nonlinear compensation risks in the industrial chain. It is matched, complementary, and nested with the main risk propagation directional manifold constructed from upstream to midstream, forming a complete dual-path risk propagation spatial structure with dominant linear propagation and supplementary nonlinear compensatory propagation as secondary pathways.

[0051] This embodiment effectively addresses the technical shortcomings of traditional techniques in identifying nonlinear and compensatory risk propagation from midstream to downstream by using temporal second-order derivative curvature estimation and a nonlinear coupling mapping function. Traditional linear monitoring models can only adapt to a single positive transmission path, ignoring the detour and compensatory risk propagation phenomena caused by the asymmetric transmission elasticity of midstream and downstream levels. By characterizing the nonlinear cumulative evolution of risk through second-order risk accumulation curvature and quantifying the mismatch deviation between the two levels through a dedicated nonlinear coupling mapping function, this embodiment identifies compensatory risk propagation branches after conventional transmission failure, fully covering the dual-mode risk propagation scenario of linear dominance and nonlinear compensation in the industrial chain, and improving the completeness of risk monitoring under complex operating conditions.

[0052] In a preferred embodiment of the present invention, step 4 includes: Step 400: In the risk feature space, calculate the intersection region of the main risk propagation direction manifold and the risk propagation compensation direction manifold, and determine the intersection region as the risk propagation convergence kernel, specifically including: Within a unified three-dimensional risk feature space comprised of operational status deviation, supply-demand gap ratio, and spatiotemporal propagation trajectory characteristics, the spatial intersection region of the risk propagation main direction manifold constructed in step 202 and the risk propagation compensation direction manifold constructed in step 302 is solved. This quantifies the range of dual-path risk coupling and superposition, ultimately pinpointing the risk propagation convergence core. This addresses the problem of ambiguous intersection region determination and inaccurate positioning caused by traditional methods that only provide qualitative descriptions without quantitative computational support. Specifically, the risk propagation main direction manifold is a two-dimensional affine subspace corresponding to linear risk propagation from upstream to midstream, carrying the dominant linear risk propagation characteristics; the risk propagation compensation direction manifold is a two-dimensional nonlinear subspace corresponding to nonlinear risk propagation from midstream to downstream, carrying the compensatory nonlinear risk propagation characteristics. Both manifolds share the same global reference point modeling origin, possessing both spatial computational uniformity and computability.

[0053] First, a unified mathematical expression for the bimanifold space is established, and then the intersection region is quantitatively solved: Principal Directional Manifold Space Equation ; Compensation Directional Manifold Space Equation ; In the formula, As the main direction of risk transmission manifold, Manifold for risk propagation compensation direction; The coordinate vector of the global reference point in the risk feature space; The first directional basis vector of the main directional manifold; It also serves as the second directional basis of the principal directional manifold and the third directional basis of the compensating directional manifold; The fourth directional basis vector of the compensating directional manifold; , , , The coefficients represent the manifold spatial extension coefficients, all taking values ​​within the continuous interval [-1, 1]. They are used to cover the risk spatial distribution under all operating conditions, from complete risk mitigation (coefficient of -1) to maximum risk extension (coefficient of 1), while eliminating invalid spatial regions that are detached from the actual risk propagation in the industrial chain. A negative coefficient indicates that the manifold extends negatively along the corresponding basis vector, corresponding to the risk mitigation attenuation condition. A zero coefficient indicates that the manifold converges to the global reference point, corresponding to the steady-state condition with no deviation in the industrial chain. A positive coefficient indicates that the manifold extends positively along the corresponding basis vector, corresponding to the worsening of risk disturbances and strong propagation conditions.

[0054] The formula for determining the intersection region of two manifolds is as follows: ; In the formula, The spatial intersection region of the primary directional manifold and the compensating directional manifold is the common spatial sub-region of the overlapping manifolds. This formula, through point-by-point spatial membership determination, selects all coordinate points that simultaneously satisfy the spatial equations of both manifolds, forming a closed, continuous, and unique spatial overlapping region. After obtaining the intersection region of the two manifolds, the mean value of all valid spatial coordinate points within the intersection region is calculated to obtain the geometric center of the intersection region. This closed, continuous intersection region... It has been identified as the risk propagation convergence core. This convergence core is the core coupled and superimposed area of ​​the linear dominant risk of the main path of the industrial chain and the nonlinear compensating risk of the auxiliary path. It has the characteristics of the greatest risk disturbance intensity, the highest risk coupling degree, and the strongest risk evolution activity, and it bears the superimposed effect of risks across the entire chain.

[0055] Step 401: Using the geometric center of the risk propagation convergence core as the origin of the envelope construction, extrapolate along the extension direction of the main risk propagation manifold and extrapolate along the extension direction of the compensation risk propagation manifold to obtain a closed envelope surface jointly enclosed by the extrapolated boundaries of the main and compensation directions. The risk characteristic space sub-region defined by the closed envelope surface is determined as the spatial boundary envelope of the risk propagation dynamic corridor, specifically including: Based on the risk propagation convergence kernel of the bimanifold intersection obtained in step 400, a complete computational process involving quantified geometric center solution, bidirectional manifold directional extrapolation, and boundary closure verification is used to adaptively construct a dynamically variable risk propagation corridor boundary envelope (the corridor being the internal region enclosed by the spatial boundary envelope). This addresses the shortcomings of traditional techniques that use fixed intervals and thresholds to characterize the risk propagation range, failing to adapt to the coupling propagation of the main and auxiliary paths in the industrial chain and nonlinear risk offset. All calculations are uniformly carried out based on the three-dimensional risk feature space (operational status deviation, supply-demand gap ratio, and spatiotemporal propagation trajectory characteristics).

[0056] Specifically, the geometric center of the risk propagation convergence core is determined and used as the sole reference origin of the dynamic corridor envelope. The convergence core is a closed, continuous spatial region formed by the overlap of two manifolds, containing multiple sets of discrete effective spatial coordinate points. The global geometric center is determined using the coordinate mean formula. This geometric center is the core reference point where the dual-path risk coupling is strongest and the risk evolution activity is highest.

[0057] The extrapolation calculation uniformly adopts the manifold spatial extension coefficient value [-1, 1] fixed in step 400, fully covering steady state, weak disturbance, strong disturbance, and risk mitigation conditions, and performs directional quantitative extrapolation on the manifold in the main direction and the manifold in the compensation direction respectively. The formula for quantization extrapolation of the manifold in the main direction is as follows: ; In the formula, All spatial coordinates of the manifold extrapolated along the main direction; This represents the coordinate vector of the geometric center of the risk propagation convergence core, i.e., the origin of the dynamic corridor envelope. By traversing all coefficient values, a global extrapolation is performed. The positive extension covers the propagation limits of strong and weak risk disturbances from upstream to midstream, while the negative extension covers the risk mitigation and decline evolution limits. Ultimately, the set of coordinates for the maximum risk propagation boundary in the main direction is output, defining the global propagation space of the dominant linear risk in the industrial chain. The manifold quantization extrapolation formula for the compensation direction is as follows: ; In the formula, This involves extrapolating all spatial coordinates of the compensation direction manifold. It traverses all discrete coefficients to complete the nonlinear spatial extrapolation, covering unconventional risk propagation paths such as nonlinear distortion, path detours, and reverse tracing after conventional transmission failures from midstream to downstream. It outputs the set of coordinates representing the maximum risk propagation boundary in the compensation direction, defining the full-domain evolution range of implicit nonlinear compensation risks in the industrial chain.

[0058] Extrapolation of boundary coordinate set in the principal direction extrapolated boundary coordinate set with compensation direction Spatial fusion fitting calculations are performed, and a spatial adjacency matching algorithm is used to complete boundary gaps and smoothly connect discrete points, constructing a high-dimensional envelope surface that is completely closed in three-dimensional space, without breaks or missing points. The closed spatial sub-region enclosed by this envelope surface is uniquely defined as the dynamic corridor for risk propagation. This region fully accommodates all risk propagation paths, feature evolution intervals, and nonlinear offset conditions under the coupling of primary and secondary paths.

[0059] The constructed dynamic corridor boundary envelope differs from the traditional fixed static risk zone. The corridor's boundary extension range, spatial coverage scale, and morphological structure are all determined by the real-time first-order risk disturbance propagation gradient and nonlinear coupling deviation. It can adaptively adjust with the dynamic changes in the intensity of upstream dominant risk disturbance and the degree of nonlinear mismatch in the midstream and downstream, conforming to the real-time risk coupling propagation state of the industrial chain. It can fully accommodate the propagation behavior of all working conditions, such as linear dominant risk, nonlinear compensation risk, and risk deviation detour.

[0060] This embodiment constructs a primary directional manifold and a compensation directional manifold, achieving a spatial geometric representation of multi-mode risk propagation. Based on a unified global reference point, a bidirectional manifold is constructed, corresponding to the propagation spaces of the primary and compensation risks respectively, enabling a spatialized, visual, and computationally comprehensible representation of the propagation patterns of different types of risks. Based on the intersection kernel of the two manifolds and the bidirectional extrapolation envelope, a dynamic and adaptive risk propagation corridor boundary envelope is generated, overcoming the problems of inaccurate characterization and poor adaptability of traditional static risk intervals. Closed risk corridors are dynamically generated based on real-time risk disturbance gradients and curvature mismatch deviations, closely aligning with the real-time risk coupling propagation range of the industrial chain, effectively improving the accuracy and dynamic adaptability of risk propagation interval definition.

[0061] In a preferred embodiment of the present invention, step 5 includes: Step 500: Within the spatial boundary envelope of the risk propagation dynamic corridor, extract each adjacent topological node pair sequentially along the topological propagation direction according to the original node connection order of the industry chain topology network. Specifically, this includes: Based on the completed modeling and solution of the risk propagation dynamic corridor spatial boundary envelope, the spatial domain of real-time effective risk propagation in the industrial chain is defined. Only the industrial chain topology within this closed envelope is determined as the effective risk transmission interval, eliminating invalid topological regions outside the envelope that have no risk disturbance, no coupling relationship, and no propagation behavior. The industrial chain topology network is a standardized network with fixed levels, unique adjacency relationships, and definite propagation directions. According to the operational logic of the physical industrial chain, it is divided into upstream supply level, midstream manufacturing level, and downstream distribution level. Each level contains multiple independent operating topological nodes, which correspond to the core units of the industrial chain such as raw material supply, component processing, finished product assembly, and market distribution. The adjacency arrangement of the nodes from top to bottom perfectly matches the positive propagation law of natural risk diffusion and step-by-step transmission. Specifically, the complete and effective topological nodes are, in order, raw material supply node, component processing node, finished product assembly node, and market distribution node. Following the forward propagation order of the topology, and based on the natural adjacency of nodes, multiple pairs of adjacent topological nodes are obtained through segment-by-segment traversal and orderly splitting. These pairs are: raw material supply node and component processing node, component processing node and finished product assembly node, and finished product assembly node and market distribution node. On this basis, a spatial validity check and screening is performed. Specifically, the multi-dimensional risk characteristic vector coordinates of the starting and ending nodes must simultaneously lie within the spatial boundary envelope of the risk propagation dynamic corridor, and the linear interpolation line connecting the two nodes in the risk characteristic space must not exceed the corridor envelope boundary. Adjacent topological node pairs that simultaneously meet both conditions are considered valid and retained. Node pairs that do not meet either condition are considered invalid pairings that exceed the envelope range and lack real-time risk transmission characteristics, and are discarded. Finally, the entire set of valid adjacent topological node pairs is obtained through screening and summarization.

[0062] Step 501: For each pair of adjacent topological nodes, calculate the Euclidean distance difference between the successor node and the predecessor node on the multi-dimensional risk feature vector, and determine the ratio of the Euclidean distance difference to the topological distance between the two nodes as the local change rate of risk intensity for the corresponding pair of adjacent topological nodes. Specifically, this includes: For each pair of valid adjacent topological nodes extracted in step 500, the degree of drastic local changes in the risk state between nodes is quantified. The rate of local change in risk intensity is defined as the core discrimination index. All calculations are based on a unified three-dimensional risk feature space, with feature dimensions including operational status deviation, supply-demand gap ratio, and spatiotemporal propagation trajectory features. Let the risk feature vector of the preceding node of any pair of adjacent topological nodes be... The risk feature vector of the subsequent node is ,in This represents the characteristic value of operational status deviation. This is a characteristic value of the supply-demand gap ratio. This represents the spatiotemporal propagation trajectory feature value. Calculate the Euclidean distance difference between the risk features of preceding and following nodes. This characterizes the magnitude of the difference in overall risk status between two nodes. Let the topological distance between two adjacent nodes be... The risk intensity local change rate is calculated as follows: The risk intensity is measured by the number of topological edges (i.e., hops) contained in the shortest path between two nodes, representing the topological span between the two nodes in the industry chain topology network. ; In the formula, The rate of change of risk intensity corresponding to adjacent topological node pairs represents the degree of change in the risk status of the industrial chain within a unit topological span. The larger the value, the more drastic the risk evolution fluctuation and the more significant the nonlinear change characteristics of the topological segment. The smaller the value, the more stable the risk status of the segment and the more uniform and continuous the evolution pattern.

[0063] Step 502: Compare the local change rate of risk intensity with the preset adaptive subdivision tolerance. For target topology segments where the local change rate of risk intensity exceeds the adaptive subdivision tolerance, perform an interval bisection subdivision operation, dividing the target topology segment into a first sub-segment and a second sub-segment at the midpoint. Recalculate the local change rate of risk intensity for the first and second sub-segments respectively. Recursively perform the interval bisection subdivision operation on sub-segments that exceed the adaptive subdivision tolerance until the local change rate of risk intensity for all sub-segments is less than or equal to the adaptive subdivision tolerance. Determine the fine tracking step size within the corresponding segment based on the topology span of each sub-segment obtained from the final subdivision. Specifically, this includes: By employing a fixed threshold discrimination and recursive binary subdivision mechanism, this method performs refined subdivision of topological segments with drastic risk fluctuations and significant state abrupt changes, addressing the technical challenge of accurately tracking risk-amplifying segments with fixed step sizes. The adaptive subdivision tolerance is determined through historical data calculation; specifically, a threshold binary iterative optimization algorithm is used to solve the problem on the entire historical risk sample dataset of the industry chain, converging to obtain the optimal threshold. Assuming that the calculated tolerance value is... Specifically, a full range of historical topological segment samples covering steady-state, weakly disturbed, and strongly abruptly changing operating conditions across the entire industrial chain for 12 consecutive months are collected. The local rate of change of risk intensity corresponding to all historical samples is calculated in batches to construct a historical rate of change sample set. The dispersion of historical risk fluctuations is quantified using the overall standard deviation statistical formula, and extreme outliers are eliminated using the normal distribution 3σ criterion to obtain an effective sample set. The iterative optimization interval is set to the minimum to maximum value of the effective samples. Prioritizing the avoidance of missed risks, an asymmetric weighted total error is constructed as the iterative objective function, with the objective function formula as follows: ,in The misclassification rate of steady-state segments (i.e., the proportion of samples in the true steady-state segment that are misclassified as abrupt change segments). The false negative rate for mutation regions (i.e., the proportion of samples that are false negatives but are not identified as steady-state regions in the actual mutation regions). The misjudgment penalty coefficient is set to 0.1 to significantly reduce the penalty for misjudgments and prioritize ensuring that no real risk mutations are missed. In each iteration, the midpoint of the interval is used as a candidate threshold, the corresponding total error is calculated, and the interval range is continuously narrowed. The iteration convergence precision is set to [value missing]. When the difference in the objective function error between two consecutive iterations is less than the convergence precision and the candidate threshold no longer undergoes numerical updates, the iteration is considered to have converged. The corresponding optimal critical threshold at this point is the precise boundary between steady-state small fluctuations and sudden, drastic fluctuations. Finally, the convergence solidifies to obtain the adaptive subdivision tolerance. Assuming the adaptive subdivision tolerance threshold... It can distinguish between normal minor risk fluctuations and abnormal sudden risk fluctuations in the industrial chain, and is adapted to the risk judgment boundary under all working conditions.

[0064] The local change rate of risk intensity for each topological segment calculated in step 501 With adaptive subdivision tolerance Compare them one by one and select the best ones. > The target abrupt topological segments are characterized by drastic changes in risk status and nonlinear abrupt changes, requiring subdivision. For each target topological segment, the segment is uniformly divided into a first sub-segment and a second sub-segment, with the midpoint of the segment's topological span as the dividing node. The topological span of each sub-segment is half that of the original segment. After subdivision, the risk feature vectors of the start and end nodes of each sub-segment are extracted. The calculation logic of step 501 is repeated to recalculate the local rate of change of risk intensity for each of the two sub-segments.

[0065] Threshold comparisons are continuously performed on all sub-segments. For sub-segments that still satisfy the condition that the local rate of change of risk intensity is greater than the adaptive subdivision tolerance, binary subdivision and rate of change recalculation operations are continuously performed until all sub-segments satisfy the condition that the local rate of change of risk intensity is less than or equal to the adaptive subdivision tolerance. After the iteration terminates, the topological span of all stable sub-segments uniformly adapts to the local risk fluctuation characteristics. The topological span of each sub-segment is uniformly determined as the fine tracking step size for high-precision state tracking of risk mutation segments.

[0066] Step 503: For aggregated topology segments where the local rate of change in risk intensity is lower than the adaptive subdivision tolerance, the current tracking step size is expanded and merged according to a preset multiplication factor. The coarse-grained tracking step size within the corresponding segment is determined by the expanded and merged topology span. The ordered set of all fine-grained tracking step sizes and all coarse-grained tracking step sizes is determined as a set of adaptive tracking step sizes, specifically including: For topology segments with stable risk status and no significant fluctuations, step size expansion and merging are performed to reduce redundant calculations while ensuring tracking accuracy, achieving an adaptive step size configuration that combines coarse and fine granularity. The preset step size multiplication factor is a fixed parameter. The value is set to 2.0, which balances the tracking efficiency of stable sections with the accuracy of risk detail preservation, and avoids the loss of risk features caused by excessive merging.

[0067] The rate of change of local risk intensity in all topological segments is less than or equal to the adaptive subdivision tolerance. The segment is identified as a stable aggregate topological segment. Such segments exhibit uniform risk evolution without abrupt shifts, and do not require fine-grained subdivision tracking.

[0068] For each stable aggregated topological segment, based on the original segment topological span and combined with the multiplication factor, an expansion operation is performed, and the coarse-grained tracking step size is calculated as follows: ; In the formula, To expand the coarse-grained tracking step size after merging, For the original stationary topological segment span, This is the step size multiplication factor. By expanding and merging the step size, adaptive amplification of the tracking step size in stable segments is achieved, reducing the number of invalid tracking samples.

[0069] All fine-grained tracking step lengths and all coarse-grained tracking step lengths obtained in step 502 are arranged and integrated in an orderly manner according to the original propagation order of the industry chain topology network to form a unique set of adaptive tracking step lengths, thus completing the adaptive configuration of the risk tracking scale.

[0070] This embodiment accurately identifies the differences in risk fluctuations across topological segments by analyzing the local rate of change of risk intensity. For segments with significant risk abrupt changes or nonlinear fluctuations, a recursive binary subdivision is used to obtain a fine-grained tracking step size. For segments with stable risk, step size expansion and merging are used to obtain a coarse-grained tracking step size, forming an adaptive step size system that combines fine and coarse-grained approaches. This ensures tracking accuracy in key scenarios such as risk abrupt changes and offset distortions, avoiding the omission of local risk abrupt changes by using fixed large step sizes. Furthermore, merging step sizes in stable segments reduces invalid sampling operations, improving the efficiency and accuracy of end-to-end risk tracking. Based on the risk diffusion intensity and evolution direction angle collected node by node, precise weight and direction attributes are assigned to each propagation edge of the topological network. The generated risk propagation path topology map can reflect the differences in risk propagation capabilities and trends across different topological segments, solving the problems of single-dimensional and dimension-defining traditional risk propagation feature representations.

[0071] In a preferred embodiment of the present invention, step 6 includes: Step 600: Using the topological centroid position corresponding to the reference point as the starting position for extrapolation, and following the order of the tracking steps in a set of adaptive tracking step sizes, the risk state extrapolation is performed segment by segment along the risk propagation dynamic corridor. At the termination node of each tracking step, the multi-dimensional risk feature vector of the corresponding node is collected, and the risk diffusion intensity value and risk evolution direction angle value are extracted from it. Specifically, this includes: Using the topologically weighted centroid position corresponding to the global reference point in the early-stage risk feature space as the unified extrapolation starting position, the uniqueness of the benchmark for risk extrapolation across the entire chain is ensured. Based on the ordered set of adaptive tracking step sizes constructed in step 503, risk state extrapolation calculations are performed segment by segment along the forward propagation direction of the industry chain topology within the boundary envelope of the risk propagation dynamic corridor, according to the step size arrangement. After traversing the topological segment corresponding to each adaptive tracking step size, the termination topological node corresponding to the current step size is located, and the complete multi-dimensional risk feature vector of the termination node in the unified three-dimensional risk feature space is collected. The three dimensions are operational status deviation, supply-demand gap ratio, and spatiotemporal propagation trajectory characteristics, respectively. The intensity of risk diffusion and the trend of risk evolution direction are represented by quantitative calculation formulas.

[0072] Specifically, the risk diffusion intensity is used to characterize the overall intensity level of the risk diffusion from the current node. It achieves a global intensity fusion representation through the spatial magnitude of the three-dimensional risk feature vector, which can integrate single-dimensional local risk fluctuations into the overall risk diffusion capability of the node, avoiding the shortcomings of one-sided single-dimensional feature representation. The specific calculation is as follows: ; In the formula, This represents the intensity of risk diffusion at the node. This represents the characteristic value of operational status deviation. This is a characteristic value of the supply-demand gap ratio. This is a characteristic value of the spatiotemporal propagation trajectory. This value is quantitatively represented by the comprehensive disturbance amplitude of three-dimensional risk dimensions: operational status deviation, supply-demand gap ratio, and spatiotemporal propagation trajectory characteristics. The larger the value, the higher the degree of operational deviation of the current node, the larger the supply-demand imbalance gap, and the more significant the spatiotemporal propagation disturbance of risk. The stronger the node's ability to penetrate, spread, and transmit risks outwards. The smaller the value, the weaker the risk disturbances in each dimension of the node, and the lower the activity and intensity of risk propagation outwards. This achieves a refined, quantifiable, and comparable accurate characterization of the node's risk diffusion intensity.

[0073] The risk evolution direction angle is used to characterize the offset direction and propagation trend of risk evolution. Using the global reference positive axis of the three-dimensional risk feature space as the zero-angle reference, the direction is quantified by the spatial angle between the node risk feature vector and the reference axis. This characterizes the degree of offset and evolution trend of the current node's risk relative to the standard steady-state propagation direction. Before specific calculations, it is first determined whether the magnitude of the current node's risk feature vector is less than a preset minimum threshold. ,like < This indicates that the node is approximately in a risk-free ideal state, and a direct judgment can be made. =0; otherwise, calculate the spatial angle using the following formula: ; In the formula, This represents the current node's risk evolution direction angle value. A steady-state baseline vector is pre-defined for the risk feature space, corresponding to the standard feature vector under steady-state propagation conditions without risk disturbances in the industrial chain. The smaller the angle, the more closely the current risk propagation direction conforms to the standard steady-state propagation trend; the larger the angle, the more significantly the risk exhibits a deviation, detour, or distorted propagation trend, thus fully realizing the quantitative representation of the risk evolution deviation direction and dynamic propagation trend. Segment-by-segment tracking and node-by-node quantitative data collection are performed, retaining real-time risk feature data for each step node throughout the process, without omissions or distortions.

[0074] Step 601: Concatenate the risk diffusion intensity values ​​and risk evolution direction angle values ​​collected at all tracking step termination nodes in the order of collection into a risk diffusion intensity value sequence and a risk evolution direction angle value sequence, specifically including: Based on the quantitative risk parameters obtained from the segment-by-segment, node-by-node time-series data collection in step 600, two sets of standardized risk feature sequences with time-series alignment, topological correspondence, and dimensional matching are constructed. Following the topological traversal order and risk extrapolation propagation order of the adaptive tracking step size, the risk diffusion intensity values ​​collected from all terminating nodes are sequentially and orderly concatenated to form a one-dimensional continuous risk diffusion intensity value sequence. This sequence fully reproduces the dynamic fluctuations, strength changes, and local mutation characteristics of risk diffusion intensity along the entire topological path from upstream to downstream of the industry chain. Simultaneously, following a completely consistent node collection time sequence and topological arrangement order, the risk evolution direction angle values ​​of all terminating nodes are sequentially concatenated to form a risk evolution direction angle value sequence. This sequence continuously records the directional shift, distortion fluctuations, and trend switching characteristics during the entire risk propagation process. The two sets of sequences have the same number of nodes, one-to-one time sequence, and perfectly matched topological positions, comprehensively depicting the entire linear and nonlinear risk propagation process under the coupling of the primary and secondary dual paths from two core dimensions: risk propagation amplitude intensity and risk propagation shift direction.

[0075] Step 602 involves generating a supply chain risk propagation path topology map by overlaying the risk diffusion intensity value sequence as the edge weight attribute and the risk evolution direction angle value sequence as the edge direction attribute on the supply chain topology network. This specifically includes: Based on the node connections of the original industrial chain topology network, without altering the original upstream and downstream topological adjacency order and propagation logic, the values ​​corresponding to the two sets of time-aligned risk feature sequences constructed in step 601 are sequentially assigned to each propagation edge of the topology network as dynamic weight attributes of the topology edges. The weight directly corresponds to the risk propagation amplitude and disturbance intensity of the corresponding topology segment, distinguishing the difference in propagation capability between stable propagation segments and abruptly disturbed strong disturbance segments. Simultaneously, the values ​​corresponding to the risk evolution direction angle value sequences constructed in step 601 are sequentially assigned to each propagation edge of the topology network as directional offset attributes of the topology edges, used to characterize the degree of deviation of each topology path relative to standard steady-state propagation, distinguishing between linear main path regular propagation and nonlinear compensated bypass distortion propagation. Through the superposition of these dual attributes, a topology map of the industrial chain risk propagation path, possessing topological structure, intensity weights, and evolution direction, is finally generated, achieving quantitative, visual, and refined representation of the entire link risk propagation path.

[0076] Step 603: After summing the entire risk diffusion intensity value series, take the average value. Then, weight the average risk diffusion intensity with the normalized directional offset to obtain the comprehensive risk situation index, which specifically includes: By integrating the cumulative propagation scale of risks across the entire path with the overall evolutionary shift trend, a comprehensive risk situation index is constructed that can represent the overall risk situation of the industrial chain across the entire domain, solving the problems of traditional single-point risk assessment being one-sided and unable to reflect the cumulative coupling effect. The risk diffusion intensity value sequence obtained in step 601 is summed across the entire sequence. To eliminate the impact of fluctuations in the number of sampling nodes caused by different adaptive subdivision levels under different time windows on the absolute cumulative value, the sum is divided by the total number of sampling nodes. The average risk diffusion intensity along the entire path is obtained. The formula for calculating the average risk diffusion intensity is as follows: ; In the formula, This represents the average risk diffusion intensity across the entire pathway. For the first in the sequence Risk diffusion intensity value corresponding to each topology termination node; This represents the total number of nodes in the sequence, corresponding to the total number of sampling nodes in the end-to-end adaptive tracking.

[0077] The global mean of the risk evolution direction angle value sequence is calculated to quantify the average offset distortion of the risk across the entire link. By averaging the risk offset angles of all sampling nodes along the entire path, the random fluctuation error of a single node is offset, and the average offset amplitude and distortion trend of the overall risk of the industrial chain relative to the standard linear steady-state propagation path are converged, realizing a quantitative characterization of the risk propagation offset law across the entire link. The calculation formula is as follows: ; In the formula, The mean directional angle of risk evolution along the entire path (in radians); For the first in the sequence The risk evolution direction angle value corresponding to each topology termination node. Because It has the dimension of angle (radians), while Since the intensities are dimensionless cumulative intensities, they cannot be directly weighted and added together. Therefore, for Perform dimensionless processing and divide by the maximum possible angle. (Corresponding directions are completely opposite), to obtain the normalized direction offset. ; The value range is [0,1], where 0 represents perfectly conforming to the standard steady-state propagation direction and 1 represents completely reverse offset.

[0078] Average risk diffusion intensity Normalize the historical maximum value to obtain the normalized average risk diffusion intensity. ,make and All values ​​are in the [0,1] dimension to avoid numerical dominance and imbalance. The average risk diffusion intensity (after normalization) and the normalized direction offset are fused to obtain the comprehensive risk situation index. The weighting coefficients are obtained as follows: historical risk samples covering steady state, weak disturbance, and strong distortion / abrupt change are collected to construct a fitted dataset containing real risk situation labels, historical average risk diffusion intensity, and historical normalized direction offset. Based on the real situation labels, a least squares error loss function is constructed: ; In the formula, This represents the fitting error loss value; the smaller the value, the higher the fitting accuracy. This represents the total number of historical fitted sample groups; For the first The standardized true risk status labels for the sample group are determined. Specifically, data on supply chain conditions, supply and demand, and risk incidents are collected and divided into four risk conditions with fixed value ranges: steady state (0.00-0.25), slight disturbance (0.26-0.50), moderate risk (0.51-0.75), and severe sudden change (0.76-1.00). Three standardized core quantitative indicators with clear boundaries and reproducibility are statistically analyzed within a single sample's corresponding topological segment and a fixed statistical period (uniformly set at 30 days). These indicators are: risk incident frequency (the cumulative total number of various risk incidents such as equipment malfunctions, supply chain failures, and process failures within the 30-day statistical period for that topological segment); maximum supply-demand imbalance (the largest absolute value of the supply-demand imbalance among all real-time sampling differences in upstream and downstream supply-demand matching data within the 30-day statistical period for that topological segment); and cumulative operational deviation (the point-by-point sum of operational status deviation values ​​corresponding to all equally spaced sampling times within the 30-day statistical period for that topological segment). An extreme value normalization formula is used to map the three types of original indicators to a dimensionless standard interval of 0 to 1. A fixed-weight fusion strategy is applied to the three sets of normalized indicators, with each dimension equally allocated a weight of 1 / 3. The fusion calculation formula is as follows: In the formula These are the normalized values ​​corresponding to the frequency of risk incidents, the maximum imbalance between supply and demand, and the cumulative total of operational deviations, respectively. The indicator is integrated with a temporary value; the integrated temporary value is matched with a preset working condition risk range, and a unique corresponding standardized true risk status label is obtained. and The first Historical cumulative intensity and normalization direction offset of the sample group.

[0079] limited Set the iterative convergence precision to 0. The algorithm iteratively optimizes the loss function, determining convergence when the difference between adjacent iteration errors is less than the convergence precision. The optimal weights are then fixed (example values). The formula for calculating the comprehensive risk situation index based on fixed weights is as follows: ; In the formula, This serves as the final comprehensive risk situation index; The cumulative risk intensity weight is used to characterize the scale of risk propagation and the amplitude of disturbances. The risk offset trend weighting focuses on characterizing the degree of nonlinear distortion and bypass propagation. This comprehensive index integrates the intensity of risk accumulation and the overall evolutionary offset characteristics. The larger the index value, the stronger the risk accumulation effect across the entire industrial chain, the more significant the nonlinear distortion propagation, and the more severe the overall risk situation. It can achieve a unified quantitative assessment of the overall dynamic risk situation of the industrial chain.

[0080] This embodiment constructs a comprehensive risk situation index by summing the cumulative risk intensity across the entire sequence and weighting the mean of the evolution direction. It fully integrates multi-dimensional features such as the scale of risk propagation, diffusion intensity, and evolution direction, providing a unified representation of the overall dynamic risk situation across the entire level and path of the industrial chain. Based on the effective tracking range constrained by the boundary envelope of the dynamic corridor for risk propagation, and combined with the mechanism of ordered traversal of topological nodes and adaptive step-by-step extrapolation, it avoids problems such as blind spots in risk tracking, loss of local features, and temporal breakpoints that are prone to occur in traditional technologies. It can completely capture the dynamic evolution, accumulation, and deviation of risk propagation across the entire industrial chain, achieving adaptive dynamic monitoring of the entire process of risk propagation.

[0081] like Figure 2 As shown, embodiments of the present invention also provide a supply chain risk monitoring system, including: The risk feature modeling module is used to identify three structural primitives and their corresponding multi-dimensional risk feature vectors in the industrial chain topology network; it performs weighted fusion on each multi-dimensional risk feature vector, calculates the topological centroid in the risk feature space, and marks the topological centroid as a reference point; The main propagation direction manifold construction module is used to calculate the first-order risk perturbation propagation gradient between the first and second structural primitives. When the magnitude of the first-order risk perturbation propagation gradient exceeds the dynamic stability threshold, the main risk propagation direction manifold is constructed from the reference point, which is jointly spanned by the multi-dimensional risk feature vectors of the first and second structural primitives. The compensation directional manifold construction module is used to calculate the nonlinear coupling deviation between the second-order risk cumulative curvature of the second and third structural primitives. When the nonlinear coupling deviation exceeds the curvature mismatch tolerance boundary, a risk propagation compensation directional manifold is constructed starting from the reference point, which is jointly spanned by the multi-dimensional risk feature vectors of the second and third structural primitives. The dynamic corridor boundary envelope determination module is used to determine the spatial boundary envelope of the risk propagation dynamic corridor based on the geometric intersection region of the risk propagation main direction manifold and the risk propagation compensation direction manifold in the risk feature space. The adaptive tracking step size optimization module is used to calculate the local change rate of risk intensity between adjacent topological nodes segment by segment along the topological propagation direction in the dynamic corridor of risk propagation, and determine a set of adaptive tracking step sizes. The global risk situation quantification module is used to perform segment-by-segment risk state extrapolation along the dynamic risk propagation corridor with a set of adaptive tracking step sizes, collect the risk diffusion intensity value and risk evolution direction angle value at the termination node of each adaptive tracking step size, and determine the topology map of the risk propagation path of the industrial chain and the comprehensive risk situation index.

[0082] It should be noted that this system is a system corresponding to the above method. All implementation methods in the above method embodiments are applicable to this embodiment and can achieve the same technical effect.

[0083] Embodiments of the present invention also provide a computer-readable storage medium storing instructions that, when executed on a computer, cause the computer to perform the method described above. All implementations in the above method embodiments are applicable to this embodiment and can achieve the same technical effects.

[0084] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for monitoring supply chain risks, characterized in that, The method includes: Step 1: Identify the three structural primitives and their corresponding multi-dimensional risk feature vectors in the industrial chain topology network; perform weighted fusion on each multi-dimensional risk feature vector, calculate the topological centroid in the risk feature space, and mark the topological centroid as a reference point; Step 2: Calculate the first-order risk perturbation propagation gradient between the first and second structural primitives. When the magnitude of the first-order risk perturbation propagation gradient exceeds the dynamic stability threshold, construct the risk propagation main direction manifold spanned by the multi-dimensional risk feature vectors of the first and second structural primitives, starting from the reference point. Step 3: Calculate the nonlinear coupling deviation between the second-order risk cumulative curvature of the second and third structural primitives. When the nonlinear coupling deviation exceeds the curvature mismatch tolerance boundary, construct a risk propagation compensation direction manifold spanned by the multi-dimensional risk feature vectors of the second and third structural primitives, starting from the reference point. Step 4: Based on the geometric intersection region of the main risk propagation direction manifold and the risk propagation compensation direction manifold in the risk characteristic space, determine the spatial boundary envelope of the risk propagation dynamic corridor; Step 5: Within the dynamic corridor of risk propagation, calculate the local rate of change of risk intensity between adjacent topological nodes segment by segment along the topological propagation direction, and determine a set of adaptive tracking step sizes. Step 6: Perform segmented risk state extrapolation sequentially along the risk propagation dynamic corridor using a set of adaptive tracking step lengths, collect the risk diffusion intensity value and risk evolution direction angle value at the termination node of each adaptive tracking step length, and determine the topology map of the industrial chain risk propagation path and the comprehensive risk situation index.

2. The supply chain risk monitoring method according to claim 1, characterized in that, Identify three structural primitives and their corresponding multi-dimensional risk feature vectors in the supply chain topology network, including: Traverse all nodes in the industry chain topology network and classify each node into the upstream supply layer node set, the midstream manufacturing layer node set, and the downstream distribution layer node set according to the industry chain level to which the node belongs. In the upstream supply layer node set, the node with the highest degree centrality and a primary bill of materials dependency relationship with the core products of the industrial chain is selected as the first structural element; in the midstream manufacturing layer node set, the node with the highest betweenness centrality and the function of assembling multi-source components is selected as the second structural element; in the downstream distribution layer node set, the node with the highest proximity centrality and the connection to the terminal market demand convergence port is selected as the third structural element. For the first, second, and third structural primitives, the deviation of the node's own operational status, the ratio of upstream and downstream supply and demand gaps associated with the node, and the historical spatiotemporal propagation trajectory records of risk events within the local topological neighborhood where the node is located are collected as multi-dimensional risk feature vectors for the corresponding structural primitives.

3. The supply chain risk monitoring method according to claim 2, characterized in that, The risk feature vectors of various dimensions are weighted and fused to calculate the topological centroid in the risk feature space, and the topological centroid is marked as a reference point, including: Obtain the node-level weight coefficients of the first, second, and third structural primitives in the industry chain topology network. The node-level weight coefficients are determined based on the inverse ratio of the topological distance between the corresponding structural primitive's industry chain level and the industry chain terminal consumer layer. The multidimensional risk feature vector of each structural primitive is multiplied by the corresponding node level weight coefficient to obtain the weighted risk feature vector; The three weighted risk feature vectors are superimposed in the risk feature space, and the geometric center of the resultant vector is calculated. The geometric center is determined as the topological centroid. The coordinate vector of the topological centroid in the risk feature space is marked as the reference point.

4. The supply chain risk monitoring method according to claim 3, characterized in that, Step 2 includes: Within a continuous time window, time-series difference operations are performed on the multi-dimensional risk feature vectors of the first structural primitive and the second structural primitive to obtain the first risk feature difference sequence and the second risk feature difference sequence. Perform time-series cross-correlation analysis on the first risk feature difference sequence and the second risk feature difference sequence, extract the maximum cross-correlation coefficient and the corresponding lag step size between them, take the maximum cross-correlation coefficient as the magnitude of the first-order risk perturbation propagation gradient, and take the lag step size as the propagation delay of the first-order risk perturbation propagation gradient. The magnitude of the first-order risk perturbation propagation gradient is compared with the dynamic stability threshold. When the magnitude of the first-order risk perturbation propagation gradient is greater than the dynamic stability threshold, the reference point is used as the starting point for manifold construction. The multi-dimensional risk feature vector of the first structural primitive is used as the first directional basis, and the multi-dimensional risk feature vector of the second structural primitive is used as the second directional basis. The first directional basis and the second directional basis span the risk feature space to form the main direction manifold of risk propagation.

5. The supply chain risk monitoring method according to claim 4, characterized in that, Step 3 includes: The second-order risk cumulative curvature of the second and third structural primitives is obtained by estimating the time-series second-order derivative of the multidimensional risk feature vectors of the second and third structural primitives. The second-order risk cumulative curvature of the second and third structural primitives is input into a pre-constructed nonlinear coupling mapping function to calculate the nonlinear coupling deviation; wherein, the nonlinear coupling mapping function is used to characterize the difference in asymmetric risk transmission elasticity between the midstream manufacturing layer and the downstream distribution layer. The nonlinear coupling deviation is compared with the curvature mismatch tolerance boundary. When the absolute value of the nonlinear coupling deviation is greater than the curvature mismatch tolerance boundary, the reference point is used as the starting point for manifold construction. The multidimensional risk feature vector of the second structural element is used as the third directional basis, and the multidimensional risk feature vector of the third structural element is used as the fourth directional basis. The risk propagation compensation directional manifold is spanned in the risk feature space through the third directional basis and the fourth directional basis. The curvature mismatch tolerance boundary is determined based on the maximum value of the nonlinear coupling deviation of the second-order risk cumulative curvature between the second and third structural elements during the historical stable operation period.

6. The supply chain risk monitoring method according to claim 5, characterized in that, Step 4 includes: In the risk feature space, the intersection region of the main direction manifold of risk propagation and the compensation direction manifold of risk propagation is calculated, and the intersection region is determined as the risk propagation convergence kernel; Using the geometric center of the risk propagation intersection core as the origin of the envelope construction, extrapolate the main direction along the extension direction of the risk propagation manifold and extrapolate the compensation direction along the extension direction of the risk propagation compensation manifold to obtain a closed envelope surface jointly enclosed by the main direction extrapolation boundary and the compensation direction extrapolation boundary. The risk characteristic spatial sub-region defined by the closed envelope surface is determined as the spatial boundary envelope of the risk propagation dynamic corridor.

7. The supply chain risk monitoring method according to claim 6, characterized in that, Step 5 includes: Within the spatial boundary envelope of the risk propagation dynamic corridor, each adjacent topological node pair is extracted sequentially along the topological propagation direction according to the original node connection order of the industrial chain topology network. For each pair of adjacent topological nodes, calculate the Euclidean distance difference between the successor node and the predecessor node on the multi-dimensional risk feature vector, and determine the ratio of the Euclidean distance difference to the topological distance between the two nodes as the local change rate of risk intensity for the corresponding pair of adjacent topological nodes. The risk intensity local change rate is compared with the preset adaptive subdivision tolerance. For target topology segments whose risk intensity local change rate exceeds the adaptive subdivision tolerance, an interval bisection subdivision operation is performed to divide the target topology segment into a first sub-segment and a second sub-segment at the midpoint. The risk intensity local change rate of the first sub-segment and the second sub-segment are recalculated respectively. The interval bisection subdivision operation is recursively performed on the sub-segments that exceed the adaptive subdivision tolerance until the risk intensity local change rate of all sub-segments is less than or equal to the adaptive subdivision tolerance. The fine tracking step size in the corresponding segment is determined by the topology span of each sub-segment obtained by the final subdivision. For aggregated topology segments where the local rate of change of risk intensity is lower than the adaptive subdivision tolerance, the current tracking step size is expanded and merged according to a preset multiplication factor. The coarse-grained tracking step size within the corresponding segment is determined by the expanded and merged topology span. The ordered set of all fine tracking step sizes and all coarse-grained tracking step sizes is determined as a set of adaptive tracking step sizes.

8. The supply chain risk monitoring method according to claim 7, characterized in that, Step 6 includes: Taking the topological centroid position corresponding to the reference point as the starting position for extrapolation, the risk state extrapolation is performed segment by segment along the risk propagation dynamic corridor according to the arrangement order of each tracking step in a set of adaptive tracking step. At the termination node of each tracking step, the multi-dimensional risk feature vector of the corresponding node is collected, and the risk diffusion intensity value and risk evolution direction angle value are extracted from it. The risk diffusion intensity values ​​and risk evolution direction angle values ​​collected from all tracking step termination nodes are spliced ​​together in the order of collection to form a risk diffusion intensity value sequence and a risk evolution direction angle value sequence, respectively. Using the risk diffusion intensity value sequence as the edge weight attribute and the risk evolution direction angle value sequence as the edge direction attribute, a topology map of the risk propagation path in the industrial chain is generated by superimposing it on the industrial chain topology network. The average risk situation index is obtained by summing the entire sequence of risk diffusion intensity values ​​and then weighting the average risk diffusion intensity with the normalized directional offset.

9. A supply chain risk monitoring system, wherein the system implements the method as described in any one of claims 1 to 8, characterized in that, include: The risk feature modeling module is used to identify three structural primitives and their corresponding multi-dimensional risk feature vectors in the industrial chain topology network. We perform weighted fusion of risk feature vectors from various dimensions, calculate the topological centroid in the risk feature space, and mark the topological centroid as a reference point. The main propagation direction manifold construction module is used to calculate the first-order risk perturbation propagation gradient between the first and second structural primitives. When the magnitude of the first-order risk perturbation propagation gradient exceeds the dynamic stability threshold, the main risk propagation direction manifold is constructed from the reference point, which is jointly spanned by the multi-dimensional risk feature vectors of the first and second structural primitives. The compensation directional manifold construction module is used to calculate the nonlinear coupling deviation between the second-order risk cumulative curvature of the second and third structural primitives. When the nonlinear coupling deviation exceeds the curvature mismatch tolerance boundary, a risk propagation compensation directional manifold is constructed starting from the reference point, which is jointly spanned by the multi-dimensional risk feature vectors of the second and third structural primitives. The dynamic corridor boundary envelope determination module is used to determine the spatial boundary envelope of the risk propagation dynamic corridor based on the geometric intersection region of the risk propagation main direction manifold and the risk propagation compensation direction manifold in the risk feature space. The adaptive tracking step size optimization module is used to calculate the local change rate of risk intensity between adjacent topological nodes segment by segment along the topological propagation direction in the dynamic corridor of risk propagation, and determine a set of adaptive tracking step sizes. The global risk situation quantification module is used to perform segment-by-segment risk state extrapolation along the dynamic risk propagation corridor with a set of adaptive tracking step sizes, collect the risk diffusion intensity value and risk evolution direction angle value at the termination node of each adaptive tracking step size, and determine the topology map of the risk propagation path of the industrial chain and the comprehensive risk situation index.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a program that, when executed by a processor, implements the method as described in any one of claims 1 to 8.

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