Engineering material supply chain sequential anomaly detection method

Abstract

The invention discloses a sequential anomaly detection method for an engineering material supply chain, and relates to the technical field of power grid material management, and the method comprises the following steps: obtaining the historical operation data and constraint parameters of the supply chain, and determining a node supply capability boundary; dividing the nodes into a continuous node set and an intermittent node set according to connection stability, and constructing a double-layer directed network structure; in the network structure, constructing a diffusion redistribution model based on transportation uncertainty and upstream and downstream inventory releasable degree difference, iteratively calculating node effective supply capability under the constraint of the supply capability boundary, including intermittent node effective supply capability, and correcting node opening probability accordingly; and performing seepage simulation based on the corrected node opening probability, and judging whether the supply chain is in an abnormal state or not according to the coupling relationship between the cross-layer maximum connected component scale and the critical seepage threshold offset.

Description

Technical Field

[0001] This invention relates to the field of power grid material management technology, and more specifically, to a method for detecting time-series anomalies in the engineering material supply chain. Background Technology

[0002] Existing methods for monitoring the supply chain of engineering materials typically involve statistical analysis of operational indicators such as inventory levels, delivery cycles, and the frequency of transportation delays or disruptions, triggering alerts when these indicators exceed preset thresholds. However, in actual engineering material supply networks, complex material flow relationships often exist between different nodes, with multiple nodes forming interdependent supply structures through multiple transportation paths. When the operational status of certain nodes in the supply chain changes, its impact often propagates along the supply path through the network. Therefore, relying solely on a single node or local indicators for anomaly detection is insufficient to comprehensively reflect changes in the overall supply network structure, potentially leading to inaccurate anomaly identification results.

[0003] Furthermore, in engineering material supply networks, the operational stability of different nodes often varies significantly. Some key supply nodes or core warehousing nodes can maintain stable supply over a long period, while others are affected by production capacity, transportation conditions, or phased demand, participating in material flow only during specific time periods, exhibiting intermittent supply characteristics. If the stability of node connectivity is not differentiated during supply network modeling, temporary transportation channels or intermittent nodes may form new connectivity paths in a short period, thereby masking the true impact of key node failures or channel blockages in the supply chain structure and reducing the ability to identify abnormal supply chain conditions.

[0004] On the other hand, existing technologies typically lack methods for systematically analyzing the overall structural state of the supply chain by comprehensively considering factors such as differences in node stability, inventory release capacity, and transportation uncertainties. These factors are transmitted step by step along the material flow path in the supply network and generate coupling effects, causing the actual supply capacity of nodes to exhibit dynamic changes. When transportation delays increase or inventory release capacity decreases, the overall connectivity of the supply network may change, even leading to a near-instability of the supply chain structure. Summary of the Invention

[0005] To overcome the aforementioned deficiencies of the prior art, embodiments of the present invention provide a method for detecting temporal anomalies in the engineering material supply chain, thereby addressing the problem that existing methods for detecting anomalies in the engineering material supply chain are unable to uniformly reflect the coupling relationship between changes in node supply capacity, differences in node connectivity stability, and the evolution of the supply network connectivity structure during the temporal operation process, thus making it difficult to accurately identify supply chain anomalies.

[0006] To achieve the above objectives, the present invention provides the following technical solution: Historical supply chain operation data and constraint parameters are obtained to determine the supply capacity boundaries of nodes. Based on connectivity stability, nodes are divided into continuous node sets and intermittent node sets to construct a two-layer directed network structure. In the network structure, a diffusion redistribution model is constructed based on transportation uncertainty and the difference in the releaseability of upstream and downstream inventory. Under the constraints of the supply capacity boundaries, the effective supply capacity of intermittent nodes is iteratively calculated, and the node opening probability is corrected accordingly. Based on the corrected node opening probability, seepage simulation is performed, and the coupling relationship between the scale of the maximum cross-layer connectivity component and the critical seepage threshold offset is used to determine whether the supply chain is in an abnormal state.

[0007] A method for detecting time-series anomalies in the engineering materials supply chain includes the following steps: In a preferred embodiment, determining the node supply capacity boundary includes: establishing a constraint model with edge flow as the variable under constraints of transportation capacity, throughput capacity, production capacity and safety stock, solving for the maximum feasible outflow of the node to obtain the basic supply upper bound of the node; constructing a decay coefficient for intermittent nodes based on historical shipping fluctuation coefficient and connectivity stability, and correcting the basic supply upper bound to obtain the preliminary node supply capacity boundary.

[0008] In a preferred embodiment, after obtaining the initial supply capacity boundary, the method further includes: constructing an upstream redundancy correction coefficient based on the ratio of the effective upstream quantity to the theoretical upstream quantity of the node, and correcting the initial supply capacity boundary; resolving the supply upper bound under stress scenarios such as inventory reference quantity reduction, removal of key outgoing edges, or decrease in node throughput capacity, to obtain the supply upper bound under stress scenarios; and determining the smaller value between the redundancy-corrected supply capacity and the supply upper bound under stress scenarios as the final supply capacity boundary of the node.

[0009] In a preferred embodiment, the step of dividing nodes into a persistent node set and an intermittent node set based on connectivity stability to construct a two-layer directed network structure includes: dividing the historical time period into multiple time slices, determining connectivity indicators based on the material flow in each time slice; calculating node connectivity stability indices based on upstream edge connectivity indicators, comparing the node connectivity stability indices with a preset stability threshold, and dividing nodes into persistent nodes or intermittent nodes based on the comparison results; and determining the directed edges connecting persistent nodes and intermittent nodes as cross-layer edges to form a two-layer directed network structure including a persistent node layer, an intermittent node layer, and cross-layer edges.

[0010] In a preferred embodiment, the step of dividing nodes into a persistent node set and an intermittent node set based on connectivity stability further includes: performing continuous segment decomposition on the connectivity indication sequence of edges within a historical time slice, and counting the length of continuous connected segments; determining that a node possesses segment stability when the length of a continuous segment is not less than a preset minimum continuous length threshold; counting the number of edges with segment stability among all upstream edges of a node, and calculating its proportion to the total number of upstream edges; and classifying the node into the persistent node set when the proportion is not less than a preset proportion threshold and the node's connectivity stability index is not less than a preset stability threshold.

[0011] In a preferred embodiment, the calculation process of the effective supply capacity of the intermittent node includes: calculating the release degree of node inventory based on node inventory and safety stock, and determining the difference in release degree between upstream and downstream inventory and the immediate supply limit based on the release degree of inventory at both ends of the edge; calculating the edge damping weight based on the transportation delay fluctuation index; constructing the edge diffusion coefficient based on the difference in release degree of inventory, the channel scheduling response coefficient, the channel capacity term and the damping weight, wherein the channel scheduling response coefficient is estimated by the ratio of historical actual allocation volume to channel capacity, and the channel capacity term is determined based on the maximum transportation capacity of the edge or the node throughput capacity; iteratively calculating the diffusion contribution of upstream nodes to downstream nodes based on the diffusion coefficient, and projecting it under the boundary constraints of throughput capacity and supply capacity to obtain the effective supply capacity of the node.

[0012] In a preferred embodiment, the diffusion redistribution model further includes a tail risk triggering mechanism: a high quantile threshold for historical transport delays is calculated for cross-layer edges, and when the proportion of tail occurrences is not less than the threshold, the cross-layer edge is marked as a tail risk edge. During the diffusion coefficient calculation or diffusion contribution allocation process, conservative constraints are applied to the tail risk edge. The conservative constraints specifically include attenuating and correcting the damping weight, attenuating the channel capacity term, or prohibiting the cross-layer edge from participating in diffusion contribution in the current iteration.

[0013] In a preferred embodiment, the iterative update of the diffusion redistribution model includes: performing direction screening before calculating the diffusion contribution, allowing only edges pointing from the persistent layer to the intermittent layer or edges whose stability difference meets the threshold to participate in contribution allocation; and normalizing the total amount of outgoing edge contributions of upstream nodes to ensure that their sum does not exceed the current effective supply capacity of the node.

[0014] In a preferred embodiment, the node open probability correction includes: power-law correction based on the ratio of the node's effective supply capacity to its supply capacity boundary; exponential decay correction based on the weighted average of the node's incoming edge delay fluctuations; and identification of key bridging nodes based on the proportion of nodes across layers and application of conservative decay correction.

[0015] In a preferred embodiment, determining whether the supply chain is in an abnormal state includes: constructing a node retention network through multiple random simulations based on the corrected node open probability, calculating the maximum connected component size that simultaneously includes nodes in the continuous and intermittent layers; estimating the critical seepage threshold using a unified probability scan; calculating a structural anomaly index based on the degree of decrease in the maximum connected component size relative to the baseline state and the offset of the critical seepage threshold, and determining the supply chain anomaly level based on the structural anomaly index.

[0016] The technical effects and advantages of the method for detecting time-series anomalies in the engineering material supply chain of this invention are as follows: This invention divides supply nodes into continuous nodes and intermittent nodes and constructs a two-layer network structure, which can effectively distinguish the different roles of long-term stable supply nodes and periodically fluctuating nodes in the supply network. It avoids the structural changes caused by the failure of key supply nodes due to the short-term formation of connectivity between temporary transportation paths or intermittent nodes, thereby making the structural characteristics of the supply chain operation status clearer and improving the ability to identify changes in the stability of supply chain connectivity.

[0017] Meanwhile, by establishing a diffusion redistribution model under the constraints of transportation delay fluctuations and inventory release rate differences, the node supply capacity is no longer determined solely by the node's own production capacity or inventory level. Instead, it can reflect the transmission and coupling effects of upstream inventory status, transportation conditions, and scheduling response capabilities in the supply network, thereby more realistically depicting the dynamic changes in the actual supply capacity of nodes in the network.

[0018] Furthermore, by adjusting the node opening probability based on the node's effective supply capacity and conducting seepage simulation analysis, the changes in network connectivity structure can objectively reflect the overall supply capacity decay and structural stability changes in the supply chain. By analyzing the changes in the scale of the maximum cross-layer connectivity component and the critical seepage threshold, it is possible to identify whether the supply network is approaching a state of structural instability, thereby enabling early identification of potential structural anomalies in the supply chain.

[0019] Therefore, this invention solves the problem that existing engineering material supply chain anomaly detection methods are unable to uniformly reflect the coupling relationship between changes in node supply capacity, differences in node connectivity stability, and the evolution of supply network connectivity structure during time-series operation, thus making it difficult to accurately identify supply chain anomalies. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the process for detecting timing anomalies in the engineering material supply chain, provided in an embodiment of the present invention.

[0021] Figure 2 This is a schematic diagram of a two-tier supply chain network structure.

[0022] Figure 3This is a schematic diagram illustrating the iterative convergence of the effective supply capacity of intermittent nodes.

[0023] Figure 4 This is a schematic diagram of the seepage scan results and the critical threshold offset. Detailed Implementation

[0024] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0025] Example 1, Figure 1 The present invention provides a method for detecting temporal anomalies in the engineering material supply chain, comprising the following steps: S1, obtain historical operational data and constraint parameters of the supply chain to determine the supply capacity boundaries of nodes; S2, based on connectivity stability, divides nodes into a persistent node set and an intermittent node set to construct a two-layer directed network structure; S3, In the network structure, a diffusion redistribution model is constructed based on transportation uncertainty and the difference in the release of upstream and downstream inventory. Under the constraint of the supply capacity boundary, the effective supply capacity of intermittent nodes is iteratively calculated, and the node opening probability is corrected accordingly. S4 performs percolation simulation based on the corrected node open probability, and determines whether the supply chain is in an abnormal state based on the coupling relationship between the scale of the maximum cross-layer connected component and the critical percolation threshold offset.

[0026] This embodiment targets an engineering material supply chain network consisting of supplier nodes, production nodes, warehousing nodes, transit nodes, construction nodes, and delivery nodes. It utilizes the evolution information of multi-source business data over a continuous time dimension to jointly model the node supply capacity, node temporal connectivity stability, cross-layer support relationships, and network structural vulnerability, thereby enabling continuous identification, hierarchical judgment, and risk warning of supply chain operation anomalies.

[0027] This embodiment is applicable to the detection of supply chain time-series anomalies for a single category of engineering materials. When multiple materials exist, the process is performed independently for each material category. The system uses a calendar day as its decision cycle, running once daily after midnight, once after confirming that the business data of the previous calendar day has been successfully recorded. All time is calculated in calendar days, and the unit of measurement for inventory, planned quantity, shipment quantity, arrival quantity, and unmet quantity is uniformly in tons.

[0028] It should be noted that the "temporal anomaly detection" referred to in this invention is not a one-time judgment based solely on inventory values, transportation status, or network topology at a static point in time. Rather, it is based on inventory changes, transportation delays, shipping volumes, node connectivity, and structural evolution within a continuous time window to detect anomalies in the current moment and the rolling time period. The temporality in this invention is reflected in at least the following three aspects: First, the input data has time series attributes, including daily inventory series, shipment volume series, transportation delay series, and edge-connected series; Secondly, the intermediate calculation indicators are updated on a rolling basis with the detection time, including the node supply capacity boundary, node connectivity stability, effective supply capacity, node opening probability, and critical seepage threshold reference value; Third, the output results are based on continuous detection time, dynamically determining the abnormality level of each detection time, and relying on historical normal time periods to maintain the reference baseline.

[0029] Therefore, this invention is not a static structural analysis method, but a time-series anomaly detection method for the continuous operation of the engineering material supply chain.

[0030] S1, Obtain historical operating data and constraint parameters of the supply chain, and determine the supply capacity boundary of the nodes, including: (1) Obtaining historical operating data and constraint parameters of the supply chain, and (2) Determining the supply capacity boundary of the nodes, as follows: In this embodiment, the supply chain is abstracted as a directed graph. ,in, This represents a set of nodes, where each node corresponds to a supplier, factory, warehouse, transit station, or construction site. Represents the set of edges.

[0031] Unless otherwise stated, in this embodiment, "current decision day" refers to the target calendar day for executing this method, denoted as... "180 consecutive days prior to the current decision date" refers to the interval... The period is 180 complete calendar days; "the most recent 30 days" refers to the interval. The 30 complete calendar days within a given historical date. During historical backtracking, for any given historical date... The same criteria are also used, that is, the relevant statistical windows are taken separately. and .

[0032] If there are slave nodes within the historical window To the node For valid shipping records, a directed edge is established. A valid shipment record is a shipment record that simultaneously meets the following conditions: the corresponding outbound shipment status is completed, the transport task number is not empty, and the shipment record has not been voided.

[0033] Suppliers and factories are defined as production nodes; nodes with an in-degree of 0 within the historical window are defined as source nodes.

[0034] If there are valid shipments of the same material category between the same pair of nodes, only one directed edge is established, and the statistical parameters on the edge are calculated using all valid samples of that material category on that edge. In this embodiment, calculations are performed separately for each material category, and statistics are not mixed between different material categories.

[0035] Business data is deduplicated based on the business primary key. The business primary key must include at least the order number, order line number, shipping node number, arrival node number, and transportation task number. When multiple records exist for the same business primary key, they are sorted in descending order by the last update time, and only the latest record is retained. The last update time uses the original update time field from the business system; if this field is missing, it is replaced by the inbound time field; if both are missing, the record is not included in the deduplication results. Records with canceled tasks, voided tasks, missing outbound completion times, or missing final receipt completion times are not included in the transportation time statistics. Records with inventory, planned quantity, shipped quantity, arrived quantity, or unmet quantity less than 0, as well as records with a transportation time less than 0, are directly removed.

[0036] Transportation time is calculated by transportation task number and defined as the final receipt completion time minus the actual outbound completion time for the same transportation task. When a shipment has multiple receipts, the last receipt completion time is used as the final receipt completion time. Shipment volume is assigned based on the actual outbound completion date, and arrival volume is assigned based on the final receipt completion date. Daily closing inventory is a snapshot of the book inventory at 23:59:59 each day. Multiple outbound shipments are allowed for the same order line; the cumulative outbound quantity for an order line is defined as the sum of all outbound records for that order line up to the statistical time. If multiple inventory snapshots exist for a given day, the one with the timestamp closest to 23:59:59 and no later than 23:59:59 is used. If only a supplementary snapshot exists for cross-day arrivals after 23:59:59, this supplementary snapshot is not considered part of the original daily closing inventory.

[0037] The planned total outbound quantity refers to the total planned quantity for which the planned outbound date falls within the statistical interval and the order line status is not voided. On-time completion quantity refers to the total completed outbound quantity for which the planned outbound date falls within the statistical interval and the corresponding actual outbound completion date is no later than the planned outbound date. Delayed completion quantity refers to the total completed outbound quantity for which the planned outbound date falls within the statistical interval and the corresponding actual outbound completion date is later than the planned outbound date. Outbound quantity not met is calculated at the order line level, and is the planned quantity minus the cumulative completed outbound quantity up to the statistical cutoff point, rounded to a non-negative value. For the same order line, on-time completion, delayed completion, and incomplete completion portions are allowed to coexist and are counted separately.

[0038] The "Insufficient Inventory Quantity" refers to the portion of the outbound quantity that was not fulfilled due to insufficient inventory, explicitly mapped to an insufficient inventory level by the reason code. The reason field is selected in a fixed order: first, the closure reason; then, the cancellation reason; and finally, the stockout reason. If the current field is empty or does not match the insufficient inventory reason dictionary, the next field is selected. The insufficient inventory reason dictionary is a pre-built business dictionary that contains at least reason codes expressing stockout, insufficient inventory, no stock available, and insufficient inventory. A reason code is considered to have matched the insufficient inventory reason dictionary if it is labeled as any of these four semantic categories in the deployment system. If this business dictionary is missing during deployment, the business system administrator should map historical reason codes to either "Insufficient Inventory" or "No Insufficient Inventory" before running this method. Before the mapping is completed, this portion of the record is not counted as an insufficient inventory quantity, but it is still counted as an unfulfilled outbound quantity.

[0039] Missing inventory is handled according to a unified rule. For any node with missing end-of-day inventory on a given historical day, first look backward for the most recent valid end-of-day inventory within the last 7 days; if found, that value is used. If there is no valid inventory within the last 7 days, the median of the valid end-of-day inventory samples for the last 30 days is taken; if there are still no valid samples within the last 30 days, it is recorded as 0. An inventory value of 0 but with a valid source record is considered valid inventory. Here, "valid inventory record" refers to an original inventory snapshot record that meets all of the following conditions: node number is not empty, material category is not empty, inventory timestamp is not empty, inventory value is not less than 0, the record is not marked as deleted, not marked as void, and not marked as a temporary write-off record generated by system rollback. The inventory value backfilled by the aforementioned rules is only used as a statistical supplement and is not considered an original valid inventory record, and cannot be used to interrupt the determination of the number of days with "no consecutive valid inventory records".

[0040] If a node has no original valid inventory record for more than 7 consecutive days, then the dates within that consecutive missing period will not participate in any statistics dependent on historical inventory, including historical calculations of inventory releaseability and sample screening of channel scheduling response coefficients. However, statistics based on the shipping task itself will still proceed normally. Consecutive missing periods are determined based on original valid inventory records and will not be interrupted by backfilling values. In this embodiment, the nearest rank quantile method is used for all quantiles; for a sample size of... Ascending sequence and quantile ratio Take position The corresponding sample value. If the sample size is 0 when calculating a certain quantile, the result of that quantile is recorded as empty and processed according to the missing completion rules given in the corresponding steps.

[0041] In this embodiment, each node records the current inventory, maximum daily outbound processing capacity, and safety stock level, as detailed below: Current inventory is recorded as , representing a node On the current decision date The latest closing inventory is used; "latest closing inventory" is uniformly defined as no later than the decision date. The closing inventory of the most recent full calendar day, i.e., the inventory taken during normal operation. Book inventory at 23:59:59, retrieved during historical recalculation. Daily 23:59:59 Book Inventory; Maximum daily outbound processing capacity is denoted as , representing a node The maximum total outbound volume that can be completed in a single day; Safety stock level is denoted as , representing a node The minimum inventory level that should be maintained.

[0042] For production nodes, the maximum daily production fulfillment capacity is also recorded, denoted as . This indicates the maximum new quantity of production that can be directly converted into available supply within the current decision-making day.

[0043] Each edge records the maximum daily transport capacity, average transport time, and standard deviation of transport time, denoted as follows: , and ,in, Representing an edge The maximum daily transport volume that can be completed. This represents the average sample of effective transportation time over the past 30 days. This represents the corresponding sample standard deviation, which is the sample standard deviation.

[0044] Missing parameters are filled in according to the following rules, specifically: 1) When a node's maximum daily outbound processing capacity is missing, the 95th percentile of the node's total daily outbound volume over the past 30 days is used; if there are no outbound records in the past 30 days, it is recorded as 0. When a production node's maximum daily production fulfillment capacity is missing, the maximum total daily outbound volume of the node over the past 30 days is used; if there are no outbound records in the past 30 days, it is recorded as 0. When an edge's maximum daily transportation capacity is missing, the maximum daily shipment volume of that edge over the past 30 days is used; if there are no valid shipments, it is recorded as 0.

[0045] 2) When the average transport time and standard deviation of an edge are missing, if the edge has at least 5 valid transport tasks in the past 30 days, the average transport time is calculated directly from the edge sample. If there are fewer than 5, the average transport time is taken as the median of the valid transport time samples of all edges in the current material category in the past 30 days, and the standard deviation of the edge transport time is taken as the median of the standard deviation samples of edge-level transport time of all edges in the current material category. Here, "standard deviation samples of edge-level transport time" means that the sample standard deviation is calculated separately for each edge with at least 2 valid transport samples, and then the median is taken after combining these edge-level standard deviations into a sample set. If there are no valid transport samples in the entire network, the average transport time of the edge is taken as 1 day, and the standard deviation of the edge transport time is taken as 0 days.

[0046] 2. Determine the node supply capacity boundary, including: First, node connectivity stability is calculated based on historical connectivity data, providing a basis for node classification and adjustment of node supply capacity boundaries. The historical time period is divided into multiple time slices, and connectivity indicators are determined based on the material flow within each time slice, including: The historical data for the 180 consecutive days prior to the current decision date is divided into 90 non-overlapping two-day time slices in calendar day order. The time range corresponding to each time slice is denoted as ,in, Construct a time-slice graph based on the nodes and edges that occur within each time slice. ,in, Indicates the first Each time slice contains a set of nodes representing business activities. Indicates the first Within each time slice, there exists a set of edges that are effectively dispatched. For each edge... and each time slice The cumulative shipment volume within the time slice is calculated based on the actual date of shipment completion. If the cumulative shipment volume is not less than 3 tons, the edge is considered connected within that time slice and recorded as a connectivity indicator. Otherwise, it is recorded as a connectivity indicator. Missing shipping data will not be imputed; it will be treated as 0.

[0047] Node connectivity stability indices are calculated based on upstream edge connectivity indicators, and these indices are compared with preset stability thresholds. Based on the comparison results, nodes are classified as either persistent or intermittent nodes, including: For each non-source node, take its upstream neighbor set. ,in, Represents all nodes that directly point to each other. The set of upstream nodes. Node connectivity stability is denoted as... , representing a node The average connectivity of all upstream edges over all time slices is defined as follows: For the source node, since there is no supply connectivity constraint from upstream, its connectivity stability is fixed at 1. In one embodiment, based on the comparison between the node connectivity stability and a preset stability threshold (preferably 0.9 in this embodiment), the node is classified as a continuous node if its connectivity stability is not lower than the preset stability threshold, and otherwise as an intermittent node.

[0048] Preferably, segment stability is further calculated based on connectivity frequency. For each upstream edge, the connectivity indicator sequence over 90 time slices is decomposed into continuous segments in chronological order; adjacent time slices with consecutive values ​​of 1 constitute a connected segment. If an upstream edge has at least one connected segment with a length of not less than 3 time slices, then the edge is considered to possess segment stability. For nodes... The number of upstream edges that possess paragraph stability is denoted as The stable proportion of paragraphs is denoted as Defined as If a node's connectivity stability is not less than 0.85 and its segment stability ratio is not less than 0.6, the node is marked as a persistent node; otherwise, it is marked as an intermittent node. This marking result is used in step S2 to construct the persistent node set. With intermittent node set .

[0049] After obtaining the node classification results, a single-node outflow constraint model is established for each node. Let the edges... The planned shipment volume as of the current decision date is ,in For decision variables in a single-node outflow constraint model, the constraints include: edge transportation capacity constraints. Constraints on daily outbound processing capacity of nodes Safety stock constraints and nonnegativity constraints For production nodes, production fulfillment constraints are also added. Under the above constraints, the goal is to maximize the total outflow of the node on that day. To achieve the goal, find the upper bound of the node-based supply. ,in, Represents a node This method considers only local inventory, outbound processing capacity, transportation capacity, and production fulfillment capacity to determine the maximum daily supply capacity. If multiple edge-level feasible solutions correspond to the same maximum total outflow value, this method only retains the node-level objective value. As subsequent input, it is not required to uniquely determine the edge-level allocation solution.

[0050] Then calculate the node's shipment fluctuation coefficient. Take the daily total outbound volume sequence of the node for the most recent 30 days, and denote it as the node number. The total outbound volume for the day was ,in This represents the sequence number of natural days within the most recent 30-day window, sorted from earliest to latest. Dates with no outbound records are counted as 0. The average daily outbound volume for the most recent 30 days is calculated based on this sequence. and standard deviation And calculate the shipping fluctuation coefficient. If there are fewer than 10 days with outbound records within the last 30 days, the shipping fluctuation coefficient is fixed at 1.

[0051] For intermittent nodes, a stability decay coefficient is introduced to weaken their supply boundary. The node stability decay coefficient is denoted as... Defined as When a node belongs to the intermittent node set, the initial supply capacity boundary of the node is denoted as... The value is When a node belongs to a persistent node set, the initial supply capacity boundary of the node is directly taken as the upper bound of the basic supply, i.e. .

[0052] After obtaining the initial supply capacity boundary, preferably, upstream redundancy correction can be further performed. An upstream redundancy correction coefficient is constructed based on the ratio of the effective upstream quantity to the theoretical upstream quantity of nodes, and the initial supply capacity boundary is corrected, including: node The theoretical upstream set is denoted as This indicates that all points directly to the node. The set of upstream nodes; the average daily inflow of each node over the past 30 days is denoted as Statistics are based on the final delivery date, with dates without delivery records counted as 0. When a node has no theoretical upstream, the redundancy correction factor is set to 1. When a node has a theoretical upstream, the average daily inflow is first evenly distributed according to the theoretical upstream quantity to obtain the single upstream baseline load. .

[0053] For any upstream node If its initial supply capacity boundary is not lower than the benchmark capacity, and it has actually supplied to the node for at least 3 days in the last 30 days. Shipment, then the node is determined. For nodes The effective upstreams. All effective upstreams constitute the effective upstream set. The upstream redundancy ratio is denoted as... Defined as The redundancy correction factor is denoted as... Defined as The revised supply capacity frontier is denoted as... The value is .

[0054] Preferably, the supply upper bound can also be resolved under stress scenarios. For ease of description, the current inventory... As a reference for node inventory, it includes: The first scenario is the reduction of the reference inventory level, which involves replacing the reference inventory level at the node with... Then, under the same constraints, the single-node outflow constraint model was resolved to obtain the upper bound of supply in the inventory reduction scenario. .

[0055] The second scenario is the critical outgoing edge removal scenario. Here, a critical outgoing edge is defined as the outgoing edge with the highest average daily shipment volume over the past 30 days for that node. The average daily shipment volume is statistically assigned based on the actual outbound completion date. In case of ties, the first outgoing edge is selected in ascending order of the destination node number. If the destination node number is a pure numeric string, it is compared in ascending numerical order; if it contains letters or other characters, it is compared in lexicographical order according to the standard string. The maximum daily transport capacity of this edge is temporarily set to 0, and the solution is recalculated to obtain the upper bound of the supply for the critical outgoing edge removal scenario. .

[0056] The third scenario is a decrease in node throughput, where the node's maximum daily outbound processing capacity is replaced with... After resolving, the upper bound of the supply for scenarios with reduced processing capacity is obtained. .

[0057] The minimum value of the results for the three scenarios is defined as the upper bound of stress supply, denoted as... ,Right now If upstream redundancy correction is used, the final supply capacity boundary of the node is denoted as... Defined as If upstream redundancy correction is not used, then it can be directly taken. .

[0058] S2 divides the nodes into a persistent node set and an intermittent node set based on connectivity stability, and constructs a two-layer directed network structure.

[0059] The edges between persistent nodes constitute the set of edges within the persistent layer. ; The edges between intermittent nodes constitute the inner edge set of the intermittent layer. ; The edges connecting persistent nodes and intermittent nodes form a cross-layer edge set. .

[0060] This results in a two-layer directed network structure containing a persistent node layer, an intermittent node layer, and cross-layer edges. For example... Figure 2As shown in the diagram, the engineering material supply chain forms a two-layer directed network structure under the current material category. Nodes are represented by letters: S for supplier nodes, F for factory nodes, W for warehouse nodes, T for transit nodes, and C for construction nodes; node numbers indicate specific node instances. Solid lines represent edges within the continuous layer, dashed lines represent edges within the intermittent layer, and dotted lines represent cross-layer support edges. The continuous node layer includes the main supply chain paths; the intermittent node layer includes supplementary supply paths with higher volatility; cross-layer support edges represent the support and replenishment relationship between the continuous node layer and the intermittent node layer. This diagram visually demonstrates the hierarchical organization and cross-layer linkage characteristics of the supply chain network.

[0061] S3. In the network structure, a diffusion redistribution model is constructed based on transportation uncertainty and the difference in the release of upstream and downstream inventory. Under the constraint of the supply capacity boundary, the effective supply capacity of intermittent nodes is iteratively calculated, and the node opening probability is corrected accordingly.

[0062] In this embodiment, the difference in upstream and downstream inventory release capacity is represented by the difference in upstream and downstream inventory release capacity. First, the node inventory release capacity, the edge inventory release capacity difference, and the node's immediate supply limit are calculated.

[0063] The release rate of node inventory is denoted as , representing a node The relative level of available inventory on the current decision date is defined as follows: When the current inventory is 0, the inventory release rate is 0.

[0064] opposite side The difference in the availability of upstream and downstream inventory is denoted as Defined as This quantity is used to characterize the supply-demand advantage of upstream nodes relative to downstream nodes.

[0065] The node's immediate supply limit is denoted as For production nodes, take... For non-production nodes, take .

[0066] Due to their high connectivity and supply stability, persistent nodes are no longer iteratively calculated for effective supply capacity in the diffusion redistribution model. Their effective supply capacity is directly approximated by the supply capacity boundary and participates in diffusion contribution and subsequent seepage simulation as a stable supply source. For unified notation, persistent nodes... Effective supply capacity is denoted as Take directly The effective supply capacity of intermittent nodes is calculated iteratively and serves as the primary basis for subsequent adjustments to the open probability of intermittent nodes.

[0067] Then, the edge diffusion coefficient is calculated. The edge diffusion coefficient is constructed based on the inventory releaseability difference, channel scheduling response coefficient, channel capacity term, and damping weight. The channel scheduling response coefficient is estimated by the ratio of historical actual allocation volume to channel capacity. The channel capacity term is determined based on the maximum edge transport capacity or node throughput capacity, including: If an edge has at least 5 effective transport missions in the last 30 days, then the edge damping weight is denoted as... Defined as ; If there are fewer than 5 samples, the edge damping weight is fixed at 0.7.

[0068] The channel scheduling response coefficient is denoted as It is estimated by the ratio of the historical actual allocation volume to the channel capacity.

[0069] For the past 30 days, daily statistics are performed: A day is included in the sample set only if both ends of a given edge have original valid inventory records, and the inventory release rate of the upstream node is higher than that of the downstream node. For dates included in the sample set, if there are no shipping records for that edge, the daily shipping volume for that edge is counted as 0. The average daily shipping volume on the sample set is divided by the edge's maximum daily transport capacity, and truncated to the interval [0,1] to obtain... ; If the sample set dates are less than 5 days, or the maximum daily transport capacity of the edge is 0, then this coefficient is fixed at 0.5. The channel capacity term is denoted as... Defined as .

[0070] The diffusion redistribution model further includes a tail risk triggering mechanism: For cross-layer edges, a high quantile threshold for historical transport delay is calculated. When the proportion of tail-end occurrences is not less than the threshold, the cross-layer edge is marked as a tail-end risk edge. During the diffusion coefficient calculation or diffusion contribution allocation process, conservative constraints are applied to the tail-end risk edge. These conservative constraints specifically include attenuating and correcting the damping weight, attenuating the channel capacity term, or prohibiting the cross-layer edge from participating in diffusion contributions in this iteration. This includes: For cross-layer edges, a tail risk triggering mechanism is introduced. For each cross-layer edge, the effective transportation duration samples of the most recent 30 days are extracted, and the 95th percentile threshold is calculated using the nearest rank quantile method, denoted as... The proportion of samples with a transportation time greater than or equal to this threshold out of the total sample size is denoted as . When there are at least 10 valid transport samples and the proportion is not less than 0.15, the edge is marked as a tail risk edge.

[0071] To impose conservative constraints on tail-risk edges, in one implementation, for edges marked as tail-risk edges on the current decision date, the edge damping weight is multiplied by 0.5, and the channel capacity term is multiplied by 0.7 before being included in the diffusion coefficient calculation. If an edge is marked as a tail-risk edge twice consecutively on both the previous and current decision dates, its diffusion contribution on the current decision date is directly recorded as 0. During the system's first run, tail-risk marking on the previous decision date is not triggered by default; from the second run onwards, the tail-risk status is persistently saved as a quadruple of material category, starting node, ending node, and decision date, and read according to the previous day's results.

[0072] The following unified rules apply to tail risk status updates: If a cross-layer edge still exists in the network on the current decision date, but the tail proportion cannot be calculated due to insufficient samples, the tail risk of that edge is marked as untriggered on the current decision date; if the edge does not exist in the network on the current decision date, no status record is generated for that day, and when it reappears, it is judged based on whether there is a continuous triggering relationship on the previous natural day with the most recent status record; if there is no status record for that edge on at least one natural day between two occurrences, the continuous triggering chain is automatically broken. During historical backcounting, backcounting is always performed day by day in historical date order, and it is allowed to overwrite old status records on the same date with backcounting results, but real-time running results are not used to overwrite historical states.

[0073] Based on the above, the edge diffusion coefficient is defined. Wherein, the edge diffusion coefficient represents the edge diffusion coefficient. The potential support strength for downstream nodes on the current decision-making date is measured in the same dimension as the supply.

[0074] The effective supply capacity of intermittent nodes is calculated using a synchronous iterative method. Let the set of intermittent nodes be... During initialization, for each intermittent node... Let the effective supply capacity of round 0 be equal to its immediate supply ceiling, denoted as ,in, Indicates intermittent nodes In the The effective supply capacity after one iteration. The maximum number of iterations is fixed at 10, and the convergence threshold is fixed at [value missing]. The support transmission coefficient is fixed at 0.6. Continuous nodes do not participate in this iteration, and their effective supply capacity remains constant throughout the solution process. .

[0075] No. During each iteration, only two types of edges are allowed to participate in diffusion: the first type is cross-layer edges whose starting point is in the persistent node set and whose ending point is in the intermittent node set; the second type is edges whose ending point is an intermittent node, whose upstream node has higher connectivity stability than the ending node, and whose connectivity stability difference is not less than 0.10. All other edges contribute 0 to diffusion in this round; edges that have triggered a two-day tail risk circuit breaker do not participate in diffusion in this round. This directional screening ensures that diffusion contributions flow only from more stable nodes or more stable layers to intermittent nodes.

[0076] For edges that satisfy the direction condition and are not blocked by circuit breakers, first calculate the unnormalized diffusion contribution. If the upstream node... If it is a persistent node, then record If the upstream node If it is an intermittent node, then denote it as... For the same upstream node, sum the unnormalized diffusion contributions of all outgoing edges that satisfy the conditions to obtain... If the sum does not exceed the effective supply capacity currently available for diffusion of the upstream node, the actual diffusion contribution of each edge is directly taken as the unnormalized value; if the sum exceeds its current effective supply capacity available for diffusion, it is normalized proportionally. Specifically, when the upstream node is a persistent node, it is taken as... When the upstream node is an intermittent node, take Through this process, the total outgoing edge contribution of upstream nodes will not exceed their current effective supply capacity.

[0077] For any intermittent node , No. The diffusion input obtained by the wheel from all upstream sources is denoted as Simultaneously, the reliability of node fulfillment is calculated. For all planned outbound tasks of the node in the most recent 30 days, the total planned outbound volume, the volume completed on schedule, the volume completed late, and the volume not completed due to insufficient inventory are statistically analyzed and recorded as follows: , , and The fulfillment rate is recorded as... The delay rate is denoted as The out-of-stock rate is denoted as The reliability of node fulfillment is denoted as... Defined as If the planned total outbound volume for the past 30 days is 0, then the fulfillment reliability is fixed at 0.5.

[0078] The candidate effective supply capacity of the intermittent node in the next round is denoted as Defined as .

[0079] The updated effective supply capacity of intermittent nodes is defined as follows: The above update is actually a projection of the candidate results under the constraints of node throughput capacity and node supply capacity boundary.

[0080] After all intermittent nodes have completed synchronization updates, calculate the maximum change between two adjacent rounds: if the following conditions are met... If the current result is not found, the iteration stops, and the current result is taken as the final effective supply capacity of the intermittent node; otherwise, the next round continues until the maximum number of iterations is reached. Figure 3 As shown in the figure, the effective supply capacity of several intermittent nodes changes with the increase of iteration rounds. The horizontal axis represents the iteration rounds of the diffusion redistribution model. The vertical axis represents the effective supply capacity of a node, in tons per day. The three curves in the figure correspond to the changing trends of the effective supply capacity of three typical intermittent nodes (e.g., node I1, node I2, and node I3) during the iterative calculation process. The circles, squares, and triangles on each curve represent the calculation results of the corresponding node in different iteration rounds. It can be seen that in the initial stage of iteration, the effective supply capacity of each intermittent node is mainly determined by the node's immediate supply limit. The decision is made as the number of iterations increases; upstream nodes gradually transfer support supply to downstream nodes through a diffusion redistribution model, and the effective supply capacity of the nodes gradually improves. When the diffusion input received by the nodes tends to stabilize, the curve gradually flattens and eventually converges, indicating that the effective supply capacity of the nodes has reached a stable state. This figure intuitively illustrates that under the combined effects of transportation uncertainty, poor inventory release rate, and fulfillment reliability, the effective supply capacity of intermittent nodes can gradually converge to a stable value through iterative calculation, thus providing a reliable basis for subsequent node opening probability correction.

[0081] In the above main implementation, continuous nodes do not participate in the iteration of effective supply capacity, but use the supply capacity boundary as a stable supply source; intermittent nodes update the effective supply capacity under the combined effects of transportation uncertainty, poor inventory release rate, channel scheduling response and contract fulfillment reliability.

[0082] As an alternative to the node effective supply capacity calculation process in the above main implementation, the following preferred implementation method can also be adopted without changing the basic input and output specifications: As a preferred implementation, in step S3, without changing the basic input, node inventory release degree, node instant supply limit, edge diffusion coefficient, tail risk correction, node absorption coefficient, supply capacity boundary and initial state quantity defined in the main implementation, an asymmetric diffusion update mechanism that prioritizes continuous nodes to support intermittent nodes can be adopted to adjust the edge contribution allocation order and intermittent node absorption method in a single iteration.

[0083] In this implementation, the edges retained in this round after screening and cycle reduction are divided into three categories according to priority: the first category is cross-layer edges from persistent nodes to intermittent nodes; the second category is intra-layer edges from persistent nodes to persistent nodes, as well as edges where the starting node's connectivity stability is higher than the ending node's and the ending node is a persistent node; the third category is the remaining edges. At the beginning of each iteration, the above classification is re-executed. If the same edge simultaneously meets the conditions of multiple categories, it is assigned to the category with higher priority.

[0084] For any upstream node, first calculate the candidate support contribution of all its retained edges. The candidate support contribution is the minimum value among the edge diffusion coefficient, the current remaining allocable supply of the upstream node in the current round, and the current remaining absorption gap of the downstream node in the current round. Then, process edges in the order of the first type, the second type, and the third type. After processing each type of edge, update the current remaining allocable supply of the upstream node and the current remaining absorption gap of the corresponding downstream node, and then process the next type of edge. If the sum of the candidate support contributions of a certain type of edge exceeds the current remaining allocable supply of the upstream node, then scale the edges of that type proportionally so that the sum of the actual support contributions of that type of edge equals the current remaining allocable supply.

[0085] Furthermore, a minimum supply constraint is imposed on persistent nodes. After a persistent node completes the support allocation for all types of edges in this round, its updated remaining allocable supply is not less than a preset proportion of its immediate supply limit; if it is less than the preset proportion, the actual support contribution of all outgoing edges of the persistent node in this round is reduced by a uniform proportion until the minimum supply constraint is met.

[0086] For intermittent nodes, the input received in a given round is divided into cross-layer input from persistent nodes and other inputs. The effective absorption of an intermittent node is obtained by differentially weighting these two input components using its node absorption coefficient. Cross-layer input from persistent nodes is weighted more heavily, while other inputs are weighted less heavily, thus increasing the priority of persistent nodes in fulfilling their support for intermittent nodes. The effective absorption of a persistent node is still determined by the total input and its node absorption coefficient.

[0087] After obtaining the effective absorption capacity of the nodes, the update order of the effective supply capacity of the nodes, the residual absorption gap, and the remaining allocable supply is consistent with the main implementation method. That is, the effective supply capacity of the nodes is updated under the constraints of the supply capacity boundary and the node throughput capacity, and the residual absorption gap and the remaining allocable supply are updated simultaneously. After each round of updates, the maximum change in the effective supply capacity of the nodes in the two adjacent rounds is used to determine whether convergence has occurred. When the preset convergence condition is met, the result of the current round is output as the final result.

[0088] In this way, without changing the basic input and core state definitions, the priority support role of persistent nodes for intermittent nodes can be improved, and the role of the persistent layer as a stable support source can be strengthened through the guaranteed supply constraint of persistent nodes and the differentiated absorption mechanism of intermittent nodes.

[0089] As another preferred implementation, in step S3, without changing the basic inputs, node inventory release rate, node instantaneous supply limit, edge diffusion coefficient, tail risk correction, node absorption coefficient, and basic state update rules defined in the main implementation, a phased update mechanism of continuous layer first and intermittent layer last can be adopted. This implementation divides the calculation of the effective supply capacity of the node at the current detection time into a continuously executed continuous layer update phase and an intermittent layer update phase.

[0090] During the persistent layer update phase, only the persistent node set is iteratively updated. Edges participating in the support contribution calculation include intra-layer edges between persistent nodes and edges pointing from intermittent nodes to persistent nodes that satisfy a preset stability difference threshold. For the latter, to suppress the reverse perturbation of the persistent layer by intermittent nodes, a preset attenuation coefficient can be applied to its corresponding edge diffusion coefficient. In this phase, persistent nodes can act as both upstream support nodes and updated nodes; intermittent nodes only participate in the calculation as input sources, and their state remains unchanged during this phase. After the persistent layer update phase ends, the frozen effective supply capacity of the persistent nodes at the current detection time is obtained.

[0091] During the intermittent layer update phase, only the set of intermittent nodes is iteratively updated. Edges participating in the support contribution calculation include cross-layer edges from persistent nodes to intermittent nodes, and intra-layer edges between intermittent nodes that satisfy the stability difference direction requirement. Persistent nodes participate in the calculation as frozen exogenous support sources during this phase, and their total available output is fixed at the frozen effective supply capacity of the corresponding node at the end of the persistent layer update phase, remaining unchanged in each iteration of this phase. However, within a single iteration, the sum of the actual support contributions of a persistent node to all its outward edges still does not exceed the total available output. Intermittent nodes are still dynamically updated according to the main implementation method.

[0092] Furthermore, during the intermittent layer update phase, the input received by the intermittent node can be divided into input from the persistent node and input from other intermittent nodes. The effective absorption of a node is obtained by weighting these two parts of the input using the node absorption coefficient, where input from the persistent node is given a higher weight, and input from the intermittent node's internal propagation is given a lower weight, to reflect the priority of the persistent layer input on the intermittent layer recovery.

[0093] After obtaining the effective absorption capacity of intermittent nodes, the effective supply capacity, residual absorption gap, and remaining allocable supply capacity of intermittent nodes are updated according to the main implementation method. After the intermittent layer update phase ends, the effective supply capacity of continuous nodes takes the frozen result of the continuous layer update phase, and the effective supply capacity of intermittent nodes takes the final result of the intermittent layer update phase, thus forming the final effective supply capacity of all nodes in the network at the current detection time.

[0094] By using the phased update method described above, the persistent layer can first form a relatively stable support foundation, and then drive the response of the intermittent layer. This reduces the coupling complexity caused by mutual feedback between the persistent and intermittent layers within the same cycle, and improves the clarity of the state propagation direction and the interpretability of the results.

[0095] After obtaining the effective supply capacity of nodes, the node opening probability is adjusted. The baseline node opening probability is denoted as... Determined by the node connectivity stability, it is defined as follows: All nodes undergo probability adjustments, but persistent and intermittent nodes are assigned their respective effective supply capacities. If node If it is a persistent node, then take ; If node If it is an intermittent node, then take This is the result after the aforementioned iteration converges.

[0096] First, a power-law correction is performed based on the ratio of the effective supply capacity of each node to the supply capacity boundary, resulting in... .

[0097] Then, using the average daily shipment volume of each country entering the border over the past 30 days as weights, the weighted mean of the standard deviation of the border transit time and the weighted mean of the average border transit time were calculated, denoted as follows: and If the sum of the average daily shipments of all inbound countries over the past 30 days is 0, then we take 0 and 1 respectively.

[0098] The probability after exponential decay correction is denoted as: .

[0099] Finally, key bridging nodes were identified and conservative attenuation corrections were applied. The set of associated cross-layer edges is denoted as , indicating the relationship with the node All cross-layer edges associated with a node, including both incoming and outgoing edges; The set of all associated edges is denoted as , indicating the relationship with the node All connected edges, including incoming and outgoing edges. The proportion of cross-layer edges is denoted as... Defined as .

[0100] A node is identified as a bridging critical node when its total number of associated edges is not less than 3 and the proportion of cross-layer edges is not less than 0.4, and a conservative attenuation coefficient is applied. To obtain the final open probability If the bridging critical node conditions are not met, the final open probability of the node is directly taken as... .

[0101] S4 performs percolation simulation based on the corrected node open probability, and determines whether the supply chain is in an abnormal state based on the coupling relationship between the scale of the maximum cross-layer connected component and the critical percolation threshold offset.

[0102] On a two-layer directed network, Monte Carlo seepage simulations are performed with the node's eventual open probability. In one implementation, the number of simulations is fixed at 1000. A 32-bit unsigned integer master random seed is generated and persisted during system initialization. Sub-seeds are derived using a fixed rule: the date, simulation number, and probability level index are concatenated into a string in the order of "8-digit year-month-day integer - simulation number - probability level index," the checksum is calculated using CRC32, and then XORed bitwise with the master random seed to obtain a 32-bit sub-seed. The CRC32 implementation uses the standard implementation corresponding to the IEEE 802.3 standard polynomial 0x04C11DB7, and the output is interpreted as an unsigned 32-bit integer. The random number generator consistently uses the MT19937 algorithm, and uniform random numbers are generated by dividing the 32-bit unsigned integer output by this algorithm by... Mapping to interval When calculating the current decision date, the probability tier index is fixed at 0; during unified probability scanning, the probability tier index is numbered from 1 to 20 according to the open probability tiers. Different probability tiers use different sub-seeds, and the same input under the same system version yields the same random sequence.

[0103] In each simulation, an interval is generated for each node. A uniformly random number is generated on the network; if the random number is less than the final open probability of the node, the node is in an open state; otherwise, it is in a closed state. An edge is retained only if both its start and end points are open in this simulation, forming a node retention network for this simulation. This retention network is then undirected, and all weakly connected components are calculated. If a connected component contains at least one persistent node and at least one intermittent node, it is considered a cross-layer connected component. The cross-layer connected component with the largest number of nodes in this simulation is selected, and its size is denoted as . ,in This indicates the Monte Carlo simulation round; if no cross-layer connected components exist, this value is recorded as 0. The average size of the largest cross-layer connected component is obtained by averaging all simulation results. Divide by the total number of current network nodes to obtain the normalized maximum cross-layer connected component size. .

[0104] To calculate the degree of decline relative to normal operating conditions, a baseline state is first established. In one implementation, during system initialization, a 30-day baseline interval is searched in available historical data. Candidate intervals must simultaneously meet the following conditions: the proportion of unfulfilled outbound shipments to the total planned outbound shipments for the day is no higher than 5% daily within the interval; if the total planned outbound shipments for the day are 0, this proportion is treated as 0; there are no business records within the interval whose operation type codes belong to emergency procurement, temporary detours, or manual forced allocation; and the overall fulfillment rate of the interval, calculated by quantity, is no less than 95%. The set of operation type codes for emergency procurement, temporary detours, and manual forced allocation is provided by a pre-set business dictionary, covering at least the three business semantics of "emergency procurement," "temporary detours," and "manual forced allocation." If the deployed system does not provide this dictionary, the relevant operation types should be manually mapped to either "special scheduling operation" or "regular operation" before performing the baseline interval search; a baseline interval should not be generated before the mapping is completed.

[0105] If multiple candidate intervals meet the criteria, the interval with the closest end date to the current decision date will be selected first; if the end dates are the same, the interval with the higher overall fulfillment rate will be selected. If no candidate interval meets the criteria, all consecutive 30-day intervals will be sorted in order of the proportion of unfulfilled outbound shipments from low to high, the overall fulfillment rate from high to low, and the end date from recent to distant, and the interval ranked first will be selected as the benchmark interval. A candidate interval is only allowed to participate in the sorting if every calendar day within it can be backed by 180 complete historical calendar days; otherwise, the candidate interval will be eliminated.

[0106] Based on the defined baseline interval, the normalized cross-layer maximum connected component size is calculated daily using the same method as the current decision date. The average of all dates within this interval is then taken to obtain the baseline normalized cross-layer maximum connected component size, denoted as [missing information]. .

[0107] The node supply capacity boundary, continuous node effective supply capacity, intermittent node effective supply capacity, node opening probability, and tail risk continuous triggering status for each historical day within the baseline interval are all recalculated based on the back calculation results of the previous historical day, using data from the 180 consecutive days prior to that historical day, and are not directly applied to the results of the current decision day. If the available historical data is insufficient to simultaneously satisfy both the 180-day backtracking and the 30-day baseline interval search when the system is first launched, the anomaly level output will not be executed temporarily; only the supply capacity boundary, node classification, and opening probability will be output. Anomaly detection will be enabled once the historical data meets the minimum window requirement.

[0108] The critical seepage threshold was then estimated using a unified open probability scan. All nodes were then temporarily assigned the same open probability. ,in In one implementation, the node open probability parameter represents the probability of a node being open in a uniform probability scan. The value is incremented from 0.05 to 1.00 in increments of 0.05. For each probability level, the same 1000 random simulations as described above are repeated to obtain the corresponding normalized cross-layer maximum connected component size, denoted as . Take the condition that satisfies The minimum probability value is taken as the critical seepage threshold for the current decision date, denoted as . If none of the probability levels meet this condition, the critical seepage threshold is recorded as 1.00. Within the baseline interval, the critical seepage threshold is calculated daily using the same method and averaged to obtain the reference critical seepage threshold, denoted as [reference threshold]. The offset of the critical seepage threshold from the baseline state on the current decision date is denoted as... .

[0109] like Figure 4 As shown in the figure, the variation of the maximum connected component size across layers is illustrated under a unified open probability scan condition. The horizontal axis represents the unified open probability parameter. The vertical axis represents the normalized maximum connectivity component size across layers. The two curves in the figure represent the changing trends of network connectivity under the baseline and current states, respectively. The circular curve represents the scan result under the baseline state, and the square curve represents the scan result under the current decision day. The horizontal dashed line in the figure represents the threshold for determining the scale of cross-layer connectivity. When the scale of the normalized maximum cross-layer connectivity component reaches this threshold, the network is considered to have begun to form a stable cross-layer connectivity structure. The x-coordinate values ​​corresponding to the intersections of the two curves with this threshold line represent the critical seepage thresholds under the baseline state. and the current decision-making day critical seepage threshold When the current state curve shifts to the right, it indicates that a higher node open probability is required to form a cross-layer connectivity structure, suggesting a decrease in the structural stability of the supply chain network. The critical seepage threshold offset can be obtained by comparing the difference between the two. In addition, by combining the degree of decrease in the size of the maximum connected component across layers, anomalies in the supply chain operation status are determined.

[0110] Supply chain anomalies are determined based on the coupling relationship between the normalized cross-layer maximum connectivity component size and the critical seepage threshold offset, including: The degree of relative decrease in cross-layer size is denoted as Defined as .

[0111] The threshold offset normalization is denoted as Defined as .

[0112] The structural anomaly index is denoted as Defined as .

[0113] In one implementation, a normal state is determined when the structural anomaly index is not greater than 0.30 and the critical seepage threshold offset is not greater than 0.05. When the structural anomaly index is greater than 0.30 and the critical seepage threshold offset is not greater than 0.05, it is judged as a local anomaly. When the structural anomaly index is not greater than 0.30 and the critical seepage threshold offset is greater than 0.05, the structure is judged to be fragile. When the structural anomaly index is greater than 0.30 and the critical seepage threshold offset is greater than 0.05, it is judged as a systemic anomaly.

[0114] In summary, this invention provides a method for detecting temporal anomalies in the continuous operation of engineering material supply chains. It can simultaneously characterize inventory evolution, transportation fluctuations, changes in connectivity stability, cross-layer support propagation, and structural transition risks. It is applicable to continuous anomaly monitoring, structural risk identification, and resilience assessment in complex engineering supply chain scenarios.

[0115] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0116] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented, in whole or in part, in the form of a computer program product.

[0117] Those skilled in the art will recognize that the modules and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0118] In addition, the functional modules in the various embodiments of this application can be integrated into one processing module, or each module can exist physically separately, or two or more modules can be integrated into one module.

[0119] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

[0120] In conclusion, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for detecting temporal anomalies in an engineering material supply chain, characterized in that, Includes the following steps: Obtain historical operational data and constraint parameters of the supply chain to determine the supply capacity boundaries of nodes; Based on connectivity stability, nodes are divided into a persistent node set and an intermittent node set to construct a two-layer directed network structure; In the network structure, a diffusion redistribution model is constructed based on transportation uncertainty and the difference in the release of upstream and downstream inventory. Under the constraint of the supply capacity boundary, the effective supply capacity of intermittent nodes is iteratively calculated, and the node opening probability is corrected accordingly. Based on the corrected node open probability, percolation simulation is performed, and the coupling relationship between the maximum cross-layer connectivity component size and the critical percolation threshold offset is used to determine whether the supply chain is in an abnormal state.

2. The method for detecting time-series anomalies in the engineering material supply chain according to claim 1, characterized in that, The determination of the node supply capacity boundary includes: Under the constraints of transportation capacity, throughput capacity, production capacity and safety stock, a constraint model with edge flow as the variable is established, and the upper bound of the basic supply of the node is obtained by solving the maximum feasible outflow of the node. For intermittent nodes, a decay coefficient is constructed based on the historical shipping fluctuation coefficient and connectivity stability. The basic supply upper bound is then modified to obtain the preliminary node supply capacity boundary.

3. The method for detecting time-series anomalies in the engineering material supply chain according to claim 2, characterized in that, After obtaining the initial supply capacity boundary, it also includes: An upstream redundancy correction coefficient is constructed based on the ratio of the effective upstream quantity to the theoretical upstream quantity, and the initial supply capacity boundary is corrected accordingly. Under stress scenarios such as reduced inventory reference volume, removal of key outgoing edges, or decreased node throughput, the supply upper bound is re-solved to obtain the supply upper bound under stress scenarios. The smaller of the redundantly corrected supply capacity and the supply upper bound under the stress scenario is determined as the final supply capacity boundary of the node.

4. The method for detecting time-series anomalies in the engineering material supply chain according to claim 1, characterized in that, The method of dividing nodes into a persistent node set and an intermittent node set based on connectivity stability to construct a two-layer directed network structure includes: The historical period is divided into multiple time slices, and the connectivity instructions are determined based on the flow of materials within each time slice. The node connectivity stability index is calculated based on the upstream edge connectivity indication, and the node connectivity stability index is compared with a preset stability threshold. Based on the comparison result, the node is divided into a continuous node or an intermittent node. The directed edges connecting persistent nodes and intermittent nodes are defined as cross-layer edges, forming a two-layer directed network structure that includes a persistent node layer, an intermittent node layer, and cross-layer edges.

5. The method for detecting time-series anomalies in the engineering material supply chain according to claim 4, characterized in that, The method of dividing nodes into a persistent node set and an intermittent node set based on connectivity stability also includes: Perform continuous segment decomposition on the connectivity indicator sequence of edges within the historical time slice, and count the length of continuous connected segments; Segment stability is defined as follows: the length of a continuous segment is not less than the preset minimum continuous length threshold. Count the number of segments with stability among all upstream edges of a node, and calculate the proportion of each segment to the total number of upstream edges. When the ratio is not less than a preset ratio threshold and the node connectivity stability index is not less than a preset stability threshold, the node is included in the persistent node set.

6. The method for detecting time-series anomalies in the engineering material supply chain according to claim 1, characterized in that, The calculation process for the effective supply capacity of the intermittent nodes includes: The release rate of node inventory is calculated based on node inventory and safety stock, and the difference in release rate of upstream and downstream inventory and the immediate supply limit are determined based on the release rate of inventory at both ends of the edge. Calculate the edge damping weight based on the transportation delay fluctuation index; The edge diffusion coefficient is constructed based on the inventory release rate difference, channel scheduling response coefficient, channel capacity term and damping weight. The channel scheduling response coefficient is estimated by the ratio of historical actual allocation volume to channel capacity. The channel capacity term is determined based on the maximum edge transport capacity or node throughput capacity. The diffusion contribution of upstream nodes to downstream nodes is calculated iteratively based on the diffusion coefficient. Projection is performed under the boundary constraints of throughput and supply capacity to obtain the effective supply capacity of the nodes.

7. The method for detecting time-series anomalies in the engineering material supply chain according to claim 1, characterized in that, The diffusion redistribution model further includes a tail risk triggering mechanism: For cross-layer edges, a high quantile threshold for historical transportation delay is calculated. When the proportion of tail occurrence is not less than the threshold, the cross-layer edge is marked as a tail risk edge. In the process of diffusion coefficient calculation or diffusion contribution allocation, conservative constraints are applied to the tail risk edge. The conservative constraints specifically include attenuating and correcting the damping weights, attenuating the channel capability term, or prohibiting the cross-layer edges from participating in diffusion contributions in this iteration.

8. The method for detecting time-series anomalies in the engineering material supply chain according to claim 6, characterized in that, The iterative update of the diffusion redistribution model includes: Before calculating the diffusion contribution, a direction screening is performed, allowing only edges pointing from the persistent layer to the intermittent layer or edges whose stability differences meet the threshold to participate in the contribution allocation. The outbound contributions of upstream nodes are normalized to ensure that their sum does not exceed the current effective supply capacity of the node.

9. The method for detecting time-series anomalies in the engineering material supply chain according to claim 1, characterized in that, The node open probability correction includes: Power-law correction is performed based on the ratio of the node's effective supply capacity to its supply capacity boundary. Exponential decay correction is performed based on the weighted average of the node's incoming edge delay fluctuation. Identify key bridging nodes based on the proportion of nodes crossing layers and apply conservative attenuation correction.

10. The method for detecting time-series anomalies in the engineering material supply chain according to claim 9, characterized in that, Whether the supply chain is in an abnormal state includes: Based on the corrected node open probability, a node retention network was constructed through multiple random simulations, and the maximum connected component size that simultaneously includes nodes in both persistent and intermittent layers was calculated. Combined with unified probability scanning to estimate the critical seepage threshold; The structural anomaly index is calculated based on the degree of decrease in the maximum connectivity component size relative to the baseline state and the offset of the critical seepage threshold, and the supply chain anomaly level is determined by combining the structural anomaly index.

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