A bulk commodity industry chain high-risk node identification method and system

Abstract

The application discloses a bulk commodity industry chain high-risk node identification method and system, and belongs to the field of complex network data processing and bulk commodity risk monitoring. The method obtains a time series of prices of multi-product nodes of an industry chain, and constructs a directed weighted risk network in a rolling window. Multi-dimensional network topology indexes are calculated and normalized in the same direction, and an index weight is generated by combining overall discriminant degree and head topology separation degree, so that window risk scores and rankings are obtained. Block resampling is performed to calculate window resampling stability, and a window weight is generated in combination with a time proximity coefficient. A final risk score is obtained through double-layer weighted fusion, and a high-risk node set and its ranking are output. The system includes seven corresponding function modules. The application can effectively improve the identification accuracy and reliability of high-risk nodes.

Description

Technical Field

[0001] This invention relates to the field of commodity price risk monitoring and complex network data processing technology, specifically to a method and system for identifying high-risk nodes in the commodity industry chain. Background Technology

[0002] In the commodity supply chain, there is a directional risk transmission relationship between the prices of different products. By treating products as nodes and the risk spillover relationship between products as directed weighted edges, a network data structure for risk monitoring can be formed, and node topology indicators such as ingress strength, outgress strength, betweenness, PageRank, k-core, and clustering coefficient can be calculated accordingly.

[0003] Existing methods for identifying critical nodes typically select a single network topology indicator or combine multiple indicators using methods such as fixed weights or entropy weights. A single indicator can only reflect one aspect of the risk propagation structure of a node; fixed weights cannot change with the network structure; when determining weights based solely on the dispersion of values ​​across all nodes, even if a particular indicator produces many subtle differences among ordinary nodes, it may not be able to separate the truly critical risk nodes that require focused monitoring from the rest of the nodes.

[0004] On the other hand, the risk network obtained by the rolling time window is affected by the age of the window, sample perturbation, and model estimation errors. If the node scores from different windows are directly averaged, earlier windows and windows with unstable ranking may make inappropriate contributions to the final score. Therefore, a high-risk node identification method is needed that can simultaneously evaluate the node identification ability of network topology indicators and the reliability of risk ranking within the rolling window.

[0005] For example, the patent with announcement number CN114462095B, ​​"A method to improve the credibility of blockchain-based evidence storage of bulk commodity transaction data", has the following problem: bulk commodity transaction evidence storage data is easy to forge and lacks reliable traceability capabilities.

[0006] The problem with the patent "Method for Assessing the Risk of Default by Trading Entities in Bulk Commodity Trading Markets" with announcement number CN114820173B is that traditional assessments of bulk commodity trading only consider individuals and ignore the risk spillover effect of trading networks.

[0007] The problem with the patent "A Traceability Control Method and System Based on Bulk Commodity Trading Platform" with announcement number CN119338485B is that centralized traceability in bulk commodity trading platforms suffers from data silos, making them vulnerable to tampering and forgery.

[0008] The technical problem to be solved by this invention is: in a dynamic directed weighted risk network, how to reduce the impact of differences in topology indicator identification capabilities, difficulty in separating head nodes, and instability of rolling window sorting on the identification results of high-risk nodes, and output a set and sort of high-risk product nodes that can be used by the risk monitoring system. Summary of the Invention

[0009] The overall concept of this invention is as follows: First, a directed weighted risk network, sparsified by temporal causality testing, is constructed window by window based on multiple rolling time windows to form a dynamic network sequence. Within each window, for each network topology indicator, the "overall discriminative power" reflecting its distribution differences across all nodes and the "head topology separation" reflecting its ability to widen the gap between the head node and other nodes are calculated simultaneously. The combined value of these two values ​​is normalized to generate indicator weights, thereby obtaining the window risk score and window risk ranking for that window, constituting the first layer (indicator layer) of weighting. Subsequently, multiple block resampling operations are performed on each window, preserving the temporal structure and cross-node synchronous relationships. Each resampling completely reconstructs the network and re-runs the entire process of indicator weighting and ranking. The "window resampling stability" is quantified by the rank correlation between the original ranking and the ranking of each resampling operation. This stability is then combined with the "time proximity coefficient," which characterizes the newness of the window by exponential decay, and normalized to generate window weights, constituting the second layer (window layer) of weighting. Finally, the window risk scores of each node under multiple windows are merged according to the window weights to obtain the final risk score and output the set of high-risk product nodes and their ranking.

[0010] The two-layer weighting works synergistically: the indicator layer ensures that "only indicators that simultaneously possess overall discreteness and head separability receive high weights", and the window layer ensures that "only windows that simultaneously possess temporal relevance and resampling stability receive high weights". The two layers of normalized weights are independent of each other and are passed down level by level, so that the final score focuses on both highly identifiable indicators and highly reliable windows.

[0011] This invention provides a method for identifying high-risk nodes in a bulk commodity supply chain, executed by a computing device, comprising:

[0012] S1. Obtain the price time series of multiple product nodes in the commodity industry chain, divide multiple rolling time windows, generate corresponding directed weighted risk networks for each window, and obtain a dynamic directed weighted risk network sequence.

[0013] S2, for each directed weighted risk network, calculate multiple network topology indicators for each product node and perform unidirectional dimensionless transformation to obtain standardized values ​​of node indicators.

[0014] S3. For each network topology indicator within each rolling time window, calculate the overall discrimination based on the distribution of the standardized values ​​of the node indicators across all product nodes, and calculate the head topology separation based on the difference between the top-ranked network topology indicators and the indicators of the remaining product nodes. Combine and normalize the two to obtain the indicator weights of each network topology indicator within the rolling time window.

[0015] S4, weighted and fused the standardized values ​​of multiple node indicators for the same product node according to the indicator weight, to obtain the window risk score and window risk ranking of each product node in each rolling time window;

[0016] S5, perform multiple block resampling for each rolling time window, reconstruct the directed weighted risk network after each resampling, recalculate the network topology index, index weight, window risk score and resampling risk ranking, and calculate the window resampling stability based on the rank correlation between the original window risk ranking and the multiple resampling risk rankings.

[0017] S6. Calculate the time proximity coefficient based on the distance of each rolling time window from the latest rolling time window, combine the coefficient with the window resampling stability and normalize it to obtain the window weight of each rolling time window.

[0018] S7: Weighted fusion of window risk scores for the same product node across multiple windows according to window weights to obtain the final risk score, and output the set of high-risk product nodes and their ranking.

[0019] Preferably, in step S1, the step of generating the corresponding directed weighted risk network window by window includes: calculating the logarithmic return series for strictly positive price time series; establishing a vector autoregressive model for the return series within each rolling time window, and generating a directional spillover matrix based on the generalized prediction error variance decomposition; performing Granger causality tests on ordered product node pairs to generate a time-series causality screening matrix; performing a co-position product operation on the directional spillover matrix and the time-series causality screening matrix, setting the edge weights of directional spillover edges that fail the Granger causality test to zero, and setting the weights of self-loop edges to zero, thereby obtaining the directed weighted risk network.

[0020] Preferably, in step S2, the plurality of network topology indicators include at least three of the following: weighted outgoing strength, weighted incoming strength, weighted betweenness centrality, risk propagation PageRank, weighted k-core, and node local weighted clustering coefficient; wherein, the network topology indicators are all set such that the larger the value, the higher the importance of risk propagation of the product node.

[0021] Preferably, in step S3, calculating the overall distinguishability includes: converting the standardized values ​​of each node index corresponding to the same network topology index within the same rolling time window into node proportions; calculating the normalized information entropy based on each node proportion; and subtracting the normalized information entropy from 1 to obtain the overall distinguishability.

[0022] Preferably, in step S3, calculating the head topology separation degree includes: determining the number of head product nodes according to a preset head ratio and the total number of product nodes, ensuring that the number of head product nodes is not less than 1 and less than the total number of product nodes; sorting the node index standardized values ​​from high to low, and determining the number of head product nodes at the top of the sorted list as the head product node set; calculating the index mean of the head product node set and the remaining product node sets respectively, and dividing the difference between the two index means by the non-zero range of the network topology index to obtain the head topology separation degree.

[0023] Preferably, in step S3, the combination and normalization to obtain the index weights of each network topology index within the rolling time window includes: multiplying the overall distinguishability of the same network topology index within the same rolling time window by the head topology separation degree to obtain the original index weight score of the network topology index; dividing the original index weight score of each network topology index by the sum of the original index weight scores of all network topology indices within the same rolling time window to obtain the index weight of each network topology index, and the sum of the index weights of all network topology indices within the same rolling time window is 1; wherein, when either the overall distinguishability or the head topology separation degree is zero, the original index weight score of the corresponding network topology index is zero, and the network topology index does not participate in the weighted fusion of the window risk score.

[0024] Preferably, in step S5, the window resampling stability is the mean of the stability components corresponding to multiple effective resamplings; each stability component is obtained by interval mapping of the Kendall tau-b rank correlation coefficient between the original window risk ranking and the corresponding resampled risk ranking; the block resampling is moving block resampling or cyclic block resampling, and the same time block index is used synchronously for the return sequences of all product nodes to preserve the local time-series correlation structure within the window and the contemporaneous relationship between product nodes.

[0025] Preferably, in step S6, the time proximity coefficient decays exponentially according to the distance between the rolling time window and the latest rolling time window expressed in a unified time unit; the sum of the indicator weights within the same effective window is 1, and the sum of the window weights of all effective windows is 1; when the sum of the combined values ​​of the overall discriminative power and the head topology separation power of each network topology indicator within the same rolling time window is 0, the rolling time window is marked as an invalid indicator window; when the window resampling stability is lower than a preset stability threshold, the corresponding rolling time window is marked as a low-reliability window, and the weight of the rolling time window in the final risk score calculation is reduced.

[0026] Preferably, in step S6, combining and normalizing the coefficients with the window resampling stability to obtain the window weights of each rolling time window includes: multiplying the time proximity coefficient of the same rolling time window with the window resampling stability to obtain the original window weight score of that rolling time window; setting a validity indicator value for each rolling time window, wherein the validity indicator value of the rolling time window marked as an invalid indicator window or an invalid resampling window is 0, and the validity indicator value of the remaining rolling time windows is 1; dividing the product of the original window weight score and its validity indicator value of each rolling time window by the sum of the products of the original window weight score and its validity indicator value of all rolling time windows to obtain the window weight of each rolling time window, and the sum of the window weights of all rolling time windows is 1.

[0027] This invention also provides a high-risk node identification system for bulk commodity supply chains, applied in a computing device to implement the above-mentioned method. The system includes:

[0028] The dynamic network generation module is used to obtain the price time series of multiple product nodes in the commodity industry chain, divide multiple rolling time windows, generate corresponding directed weighted risk networks for each window, and obtain a dynamic directed weighted risk network sequence.

[0029] The topology metric calculation module is used to calculate multiple network topology metrics for each product node for each directed weighted risk network and perform unidirectional dimensionless transformation to obtain standardized node metric values.

[0030] The indicator weighting module is used to calculate the overall discrimination of each network topology indicator within each rolling time window based on the standardized value of the node indicator across all product nodes, and to calculate the head topology separation degree based on the difference between the top-ranked network topology indicator and the indicators of the remaining product nodes. The two are combined and normalized to obtain the indicator weight of each network topology indicator within the rolling time window.

[0031] The window risk calculation module is used to weight and fuse the standardized values ​​of multiple node indicators of the same product node according to the indicator weight, so as to obtain the window risk score and window risk ranking of each product node in each rolling time window;

[0032] The stability calculation module is used to perform multiple block resampling for each rolling time window. After each resampling, the directed weighted risk network is reconstructed, the network topology index, index weight, window risk score and resampling risk ranking are recalculated, and the window resampling stability is calculated based on the rank correlation between the original window risk ranking and the multiple resampling risk rankings.

[0033] The window weighting module is used to calculate the time proximity coefficient based on the distance of each scrolling time window from the latest scrolling time window, combine the coefficient with the window resampling stability and normalize it to obtain the window weight of each scrolling time window.

[0034] The system also includes a risk node output module, which is used to weight and fuse the window risk scores of the same product node in multiple windows according to window weights, obtain the final risk score, and output the set of high-risk product nodes and their ranking.

[0035] The present invention provides a method and system for identifying high-risk nodes in a bulk commodity supply chain, which, compared with the prior art, has the following advantages:

[0036] The overall discriminative power and the head topology separation jointly participate in the weighting of indicators, so that indicators that only have general discreteness but cannot differentiate the head nodes receive lower weights.

[0037] After block resampling, the network and node ranking are fully reconstructed, so that the window weights reflect the stability of the entire process from the original time series and network edge estimation to node ranking, rather than just reflecting the fluctuation of a single intermediate parameter.

[0038] The time proximity coefficient and window resampling stability are synergistically controlled across windows, enabling newer and reliably ordered windows to make a greater contribution.

[0039] Both weights are normalized, and rules for handling invalid and low-reliability windows are set to reduce the impact of the number of indicators, the number of windows, and the degenerate denominator on the final score magnitude.

[0040] The positional product operation sets the edge weights of directional overflow edges that fail the temporal causality test to zero, transforming the originally dense directional overflow matrix into a sparse directed weighted risk adjacency matrix. Compared to directly performing topological index calculations on a dense matrix, sparsification significantly reduces the number of non-zero edges that need to be stored and traversed, thereby reducing the number of operations and memory usage required for shortest path search for weighted betweenness centrality, PageRank iteration for risk propagation, weighted k-core stripping, and triangular enumeration of local weighted clustering coefficients. Since step S5 requires performing multiple block resampling operations for each rolling time window and completely reconstructing the network and recalculating all network topological indices after each resampling, the reduction in single-operational computation is amplified exponentially by the number of resampling operations and the number of windows over the entire dynamic network sequence, enabling computing devices to handle longer price time series, more product nodes, and more resampling operations with the same computing resources.

[0041] Furthermore, the rules for determining invalid indicator windows, invalid resampling windows, and low-reliability windows enable computing devices to terminate subsequent topology indicator calculations and cross-window fusion operations in advance when they detect indicator degradation, model estimation failure, or unreliable ranking in a rolling time window. This avoids consuming computing resources on invalid data and further reduces the overall invalid computing overhead of dynamic network sequences. Attached Figure Description

[0042] Figure 1 This is a flowchart of the method for identifying high-risk nodes in the commodity supply chain according to the present invention.

[0043] Figure 2 This is a diagram showing the two-layer weighting relationship of the indicator window in this invention.

[0044] Figure 3 This is a structural diagram of the high-risk node identification system for the bulk commodity supply chain of the present invention. Detailed Implementation

[0045] The following detailed implementation of a method and system for identifying high-risk nodes in a bulk commodity supply chain, in conjunction with specific embodiments, illustrates the present invention. These embodiments are for illustrative purposes only and are not intended to limit the scope of protection of the present invention.

[0046] Example 1: Implementation of a method for identifying high-risk nodes in a bulk commodity supply chain.

[0047] Combined with appendix Figure 1-2 As shown, this invention provides a method for identifying high-risk nodes in a bulk commodity supply chain.

[0048] like Figure 1 As shown, Figure 1 This is a flowchart of the method for identifying high-risk nodes in the commodity supply chain according to the present invention. Figure 2 As shown, Figure 2 This is a diagram illustrating the two-layer weighting relationship of the indicator window in this invention. It shows the complete two-layer transmission link from the indicator layer weighting to the window layer weighting and then to the final score. This is the core innovative principle architecture of this invention.

[0049] The subject and applicable objects of the method:

[0050] The high-risk node identification method for bulk commodity supply chains of this invention is executed by a computing device, including but not limited to desktop computers, servers, workstations, or electronic devices with data processing capabilities. This device includes a processor, memory, and a data interface, with the memory storing a computer program executable by the processor. The method processes price time series data from multiple product nodes in a bulk commodity supply chain. Each product in the supply chain (e.g., upstream raw materials, midstream processed products, downstream finished products, etc.) is abstracted as a product node, and the directional risk transmission relationships between products are abstracted as directed weighted edges. This transforms the supply chain risk transmission problem into a node importance identification problem on a directed weighted complex network. This method is applicable to, but not limited to, dynamic risk monitoring, key node early warning, and risk tracing in various bulk commodity supply chains such as crude oil, coal, ferrous metals, non-ferrous metals, chemicals, and agricultural products.

[0051] Step S1: Generate a dynamic directed weighted risk network sequence.

[0052] Step S1: Obtain the price time series of multiple product nodes in the commodity industry chain, divide the time into multiple rolling time windows, generate the corresponding directed weighted risk network for each window, and obtain the dynamic directed weighted risk network sequence.

[0053] In step S1, the step of generating the corresponding directed weighted risk network window by window includes: calculating the logarithmic return series for strictly positive price time series; establishing a vector autoregressive model for the return series within each rolling time window, and generating a directional spillover matrix based on the generalized prediction error variance decomposition; performing Granger causality tests on ordered product node pairs to generate a time-series causality screening matrix; performing a co-positional product operation on the directional spillover matrix and the time-series causality screening matrix, setting the edge weights of directional spillover edges that fail the Granger causality test to zero, and setting the weights of self-loop edges to zero, thus obtaining the directed weighted risk network. The specific details are as follows:

[0054] Step S1 involves converting the original price time series into a window-by-window, time-series causality-tested, sparsified directed weighted risk network, outputting a dynamic directed weighted risk network sequence as the unified input for all subsequent steps. Step S1 comprises eight steps: price acquisition and quality verification, logarithmic return calculation, rolling window partitioning, vector autoregression modeling, generalized prediction error variance decomposition, directional spillover matrix normalization, Granger causality screening, and in-place product sparsification.

[0055] (a) Price series acquisition and data quality verification.

[0056] The computing device obtains information about the commodity supply chain from a price database via a data interface. Price time series of each product node are arranged according to a uniform time frequency (e.g., daily, weekly). First, a quality check is performed on the original prices: the timestamps of each product node's price are checked for continuity, duplicate values, missing values, and zero or negative values. The unit of measurement and time index of each product node are standardized to ensure that all product nodes within the same window are strictly aligned to the same time scale. Missing, zero, or negative price values ​​are first marked as invalid observations and then processed according to preset data rules. Any missing value imputation model is only allowed to fit observations at or before the corresponding rolling window endpoint; data after the window endpoint is strictly prohibited to avoid future information leakage. Only price observations that are strictly positive and have valid timestamps are included in the subsequent logarithmic return calculation.

[0057] (ii) Calculation of logarithmic return series.

[0058] Because price levels vary significantly among different products, direct price modeling is not comparable. Therefore, the price series is first converted into a logarithmic return series. Logarithmic returns are calculated only for strictly positive adjacent prices, without adding a smoothing constant to the denominator on one side. The formula is as follows:

[0059] (1)

[0060] The parameters in equation (1) are defined as follows: To assign a product node index, , This represents the total number of product nodes. Subscript for the observation time; For product nodes At any moment Price observations, For product nodes In the adjacent previous moment Both the price observations and the value of ln must be strictly greater than zero; ln is the natural logarithm. For product nodes At any moment The logarithmic return relative to the previous time step is multiplied by a coefficient of 100 to convert it to the percentage level. No smoothing constant is added to the denominator of the one-sided calculation. Any observation with missing prices, zero prices, or negative prices that do not meet the strict positive condition are marked as invalid observations and processed according to the data rules, and are not included in the calculation of equation (1).

[0061] (III) Rolling time window division.

[0062] To characterize the dynamic evolution of the risk network over time, the logarithmic return series of the entire sample is processed according to a preset window length. The preset movement step size is used to divide the time into multiple overlapping or adjacent scrolling windows. (Based on time intervals...) The first of the window endpoints A rolling time window The included rate of return observations are:

[0063] (2)

[0064] In formula (2): Indicated by time This is the set of yield observations for all product nodes within the rolling time window at the right-hand end. This is the index for the observation time within the window, and its value ranges from... arrive consecutive integers; The scrolling window length represents the number of time observations contained within a single window (window sample size). Adjacent windows move according to a preset step size. Both the moving step size and the time increment are determined based on the price data sampling frequency and risk monitoring cycle; all product nodes within the same window use a unified time index. After sliding window by window, all windows are arranged in chronological order, and the total number of windows is recorded as follows. .

[0065] (iv) Establishment of the vector autoregression model.

[0066] A vector autoregression (VAR) model is established for the multi-node return series within each rolling time window to characterize the linear lagged linkage between the prices of multiple products, providing a model basis for subsequent risk spillover measurement. The order vector autoregressive model is represented as:

[0067] (3)

[0068] In formula (3): for Time by Composed of the returns of each product node 3D column vector, For its first First-order lag vector; The lag order of the VAR model is determined within the window by information criteria such as AIC and BIC. The index for the lag order summation. ; For the first The N×N-dimensional autoregressive coefficient matrix corresponding to the first lag, whose elements characterize the lag effect between nodes; for Moment A random perturbation (residual) vector is defined, with a mean of zero and no serial correlation. Its contemporaneous covariance matrix is ​​denoted as Σ. Model estimation uses only data up to and including the current window endpoint. The lag order is determined by the information criterion. Data after the window endpoint must not be used to ensure causal direction and backtestability in the time series.

[0069] (v) Generalized prediction error variance decomposition.

[0070] Based on the VAR model, Generalized Prediction Error Variance Decomposition (GFEVD) is used to measure the contribution of a random shock at one node to the prediction error variance of another node, thus obtaining the directional risk spillover intensity. GFEVD is independent of the variable order, making its conclusions more robust. At the step prediction level, originating from nodes Impact on nodes The unnormalized contribution of the prediction error variance is:

[0071] (4)

[0072] Among them, the numerator term With denominator Calculate according to the following formulas:

[0073] (5)

[0074] (6)

[0075] The parameters in equations (4) to (6) are defined as follows: The prediction step size (prediction level) is the prediction error variance decomposition. The summation index for the step size of the impulse response. ; Let Wold (vector moving average) represent the VAR model. The N×N dimensional impulse response coefficient matrix of order N is obtained from the autoregressive coefficient matrix of equation (3). The result is obtained recursively; Σ is the residual vector of equation (3). The N×N dimensional covariance matrix of the same period; , The first , No. One element is 1 and the rest are 0. Dimension selection (unit) vector, the superscript T indicates the transpose of the vector or matrix; The first covariance matrix Σ is the covariance matrix Σ. The diagonal element, i.e. the th element The variance of the node disturbance term, note the following. It is variance, not standard deviation; For nodes Impact impulse response at each phase for nodes The numerator of the cumulative squared contribution of the prediction error variance; For nodes exist The total prediction error variance over the step, i.e. the cumulative contribution to all sources of shock, is used as the normalized denominator. for Step next node For nodes The contribution of the generalized prediction error variance.

[0076] A specific agreement is needed regarding the indexing direction: Standard GFEVD adopts the convention that "the first index is the receiving node, and the second index is the impulse source node," that is... Indicate source For the recipient The contribution. For subsequent networks "The First Line 1 Columns represent directed edges point to The unified agreement will be followed by the next step of direction normalization.

[0077] (vi) Directional normalization of the directional overflow matrix.

[0078] To ensure that all subsequent matrices uniformly adopt the "number" Line 1 Columns represent directed edges point to According to the convention, the GFEVD contribution is transposed by subscript and normalized according to the receiver to obtain the directional spillover matrix, whose elements are:

[0079] (7)

[0080] In equation (7): For the directional overflow matrix, the first... Line 1 Column elements, representing nodes Pointing to node The normalized risk spillover intensity, i.e., the source node For the receiving node Overflow occupies node The proportion of the sum of all sources of overflow received; The receiving node in equation (4) is The source node is The GFEVD contribution, after transposition, is combined with " OK Columns are edges → The agreement is consistent with the denominator; For receiving nodes Received from all Source nodes The sum of contributions, here This is a dummy index for summing the nodes; after this normalization, for any receiving node... satisfy All subsequent matrices (including the time-series causal screening matrix and the adjacency matrix) uniformly adopt the […]. Line 1 Columns represent directed edges point to .

[0081] (vii) Granger causality test and time-series causality screening matrix.

[0082] Variance decomposition reveals the magnitude of spillover strength, but it may contain statistically insignificant spurious relationships. Therefore, a Granger causality test is performed on all ordered product node pairs to examine for "node" causality. Does historical information affect nodes? "Has significant sample period prediction increment", and based on this, a time-series causal screening matrix with only 0 or 1 values ​​is generated:

[0083] (8)

[0084] In equation (8): The first time-series causal screening matrix Line 1 Column elements, corresponding to candidate directed edges → ; For ordered node pairs " Is it The significance probability (p-value) corresponding to the "Granger cause" test; The threshold value is the preset significance level; I(·) is the indicator function, which takes a value of 1 when the condition within the parentheses is true and a value of 0 otherwise. That is, ordered node pairs that fail the test take a value of 0, and ordered node pairs that pass the test take a value of 1. Therefore, when At the significance level The next one refused no The null hypothesis of the "Granger cause" is used to determine the existence of a cause. point to Significant temporal causal relationship, =1, otherwise =0; Self-loop screening value Set all values ​​to zero.

[0085] (viii) Sparsification of co-position product and dynamic network sequence generation.

[0086] The directional overflow matrix and the temporal causality screening matrix are multiplied in the same position (element-by-element / Hadamard). The weights of directional overflow edges that fail the Granger causality test are set to zero, and the weights of self-loop edges are explicitly set to zero. This yields the directed weighted risk network adjacency matrix for each rolling window, with the following elements:

[0087] (9)

[0088] In equation (9): For the first In the directed weighted risk network adjacency matrix corresponding to each rolling time window, there are nodes... Pointing to node The weight of the directed edge; , The first The elements at the same position in the window directional overflow matrix and the temporal causality screening matrix. Element-wise multiplication ensures that: any element that fails the temporal causality test ( Edges with weights equal to 0 are set to zero; diagonal elements (self-loops) The edges are explicitly set to zero. As a result, the originally dense directional overflow matrix is ​​transformed into a sparse directed weighted risk adjacency matrix, which not only eliminates statistically insignificant pseudo-overflow edges and ensures that the edge direction is consistent with temporal causality, but also significantly reduces the computational cost of subsequent topological indices. This computational cost is amplified many times over in the multiple resampling in step five.

[0089] For all By sequentially executing equations (1) to (9) for each rolling time window, a dynamic directed weighted risk network sequence corresponding to each rolling time window is obtained. , (here) Indicates the first The adjacency network of a window, with superscript ( ) differs from equation (2) in that it represents the window observation set In another implementation, the directed weighted risk adjacency matrix of each window can be directly obtained by an external network generation device. As long as each window adopts the same set of nodes, the same edge direction convention, and comparable edge weight definition, it can directly enter the subsequent two-layer weighting process.

[0090] Step S2: Calculate and standardize node topology metrics.

[0091] Step S2 calculates multiple network topology indicators for each product node for each directed weighted risk network and performs unidirectional dimensionless transformation to obtain standardized values ​​of node indicators.

[0092] In step S2, the multiple network topology metrics include at least three of the following: weighted outgoing strength, weighted incoming strength, weighted betweenness centrality, risk propagation PageRank, weighted k-core, and node local weighted clustering coefficient; wherein, all network topology metrics are set such that higher values ​​indicate a higher degree of importance in risk propagation of the product node. The specific details are as follows:

[0093] Step S2 involves calculating node topology indicators from multiple structural perspectives, such as risk spillover, risk reception, propagation hub, global impact, core embedding, and local aggregation, on each directed weighted risk network. All indicators are then converted into dimensionless values ​​that are additive and have the same direction, becoming standardized node indicator values.

[0094] (a) Selection of multi-network topology indicators.

[0095] For each window's directed weighted risk network, calculate at least three of the following: weighted outgoing strength, weighted incoming strength, weighted betweenness centrality, risk propagation PageRank, weighted k-core, and node local weighted clustering coefficient. To enable weighted fusion of different indicators, all network topology indicators are uniformly set to a unidirectional direction, where "a larger value indicates a higher importance of risk propagation at the product node." The general calculation rules for the six indicators are as follows.

[0096] 1. Weighted intensity.

[0097] The weighted outward strength is the sum of the edge weights of all non-self-looping outward edges of a node, which characterizes the total scale of risk actively output by the node. The larger the weighted outward strength of a node, the higher the total strength of the risk spilling out of the node to downstream of the industry chain or related nodes through directed edges. Self-looping edges are removed during the calculation (diagonal elements have been set to zero in equation (9)).

[0098] 2. Weighted input strength.

[0099] The weighted ingress strength is the sum of the edge weights of all non-self-looping ingress edges of a node, characterizing the total scale of external risk input that the node bears. The larger the weighted ingress strength, the more susceptible the node is to the convergence impact of risks from other nodes in the industry chain.

[0100] 3. Weighted betweenness centrality.

[0101] Weighted betweenness centrality characterizes the degree to which a node serves as a crucial hub for risk propagation. The calculation first converts positive edge weights into propagation distances: the propagation distance is the reciprocal of the edge weight, and the distance between unconnected node pairs is taken as infinity. Then, for all ordered node pairs, the shortest paths are calculated, and the proportion of the number of shortest paths passing through the current node to the total number of shortest paths for that node pair is summed (if there are parallel shortest paths, they are counted proportionally). This yields the weighted betweenness centrality of the node. A higher value indicates that more risk propagation channels must pass through this node, and its "gateway" effect is stronger.

[0102] 4. Risk propagation PageRank.

[0103] PageRank, a algorithm for risk propagation, characterizes the global influence of nodes on the steady-state diffusion of risk on a directed weighted network. It normalizes the transition probabilities between nodes using directed edge weights, sets a damping coefficient to a fixed value greater than 0 and less than 1, and iterates the steady-state probability vector using a power-law approach. For dangling nodes with no outgoing edges, their probability mass is evenly distributed among all nodes to avoid probability leakage. The higher the steady-state probability, the stronger the node's influence on the global risk propagation.

[0104] 5. Weighted k-core.

[0105] Weighted k-core decomposition characterizes the embedding depth of a node in the core layer of the network. It uses the same predefined weighted kernel decomposition rule, peeling away nodes below a peeling threshold layer by layer according to their weighting strength (association degree). The highest kernel layer a node can retain is its weighted k-core value; the higher the kernel layer, the more central the node is in the network. The definitions of strength, degree, and peeling threshold remain unchanged across all windows and all resampling.

[0106] 6. Local weighted clustering coefficients of nodes.

[0107] The local weighted clustering coefficients of nodes characterize the degree of closure of local directed weighted triangles centered on the nodes, reflecting the risk clustering and chain transmission tendency of their neighboring structures. They are calculated using the same preset directed weighted triangle closure rule, and the weight normalization method and directed triangle type remain unchanged in all windows and all resampling.

[0108] The calculation configurations for all the above indicators (including the definition of propagation distance, PageRank damping coefficient and convergence criterion, k-core stripping threshold, weighted triangular closure rule, etc.) are all written into the configuration record and saved along with the recognition results to ensure strict comparability between results from different windows and different resampling. In actual implementation, at least three of the above six indicators can be selected, or other topological indicators that conform to the directional agreement can be added while maintaining the principles of "same direction, additive, and comparable".

[0109] (ii) Dimensionless transformation in the same direction (range standardization).

[0110] Because the dimensions and value ranges of the various topological indicators differ, and some indicators naturally have opposite directions, they need to be homogenized and dimensionless first. First, all indicators are unified to the direction that "the larger the value, the higher the importance of risk transmission" (original indicators with opposite directions are first reversed), and then range standardization is used to map them to the [0,1] interval. In each window, the node The The standardized values ​​of the node metrics for each topology metric are:

[0111] (10)

[0112] In formula (10): Subscripts for network topology metrics. , The actual number of topology indicators selected ( ); For the first Nodes in a window In the The original index values ​​that have already undergone homogenization on each topological index; , The first The first window Each indicator in all The maximum and minimum values ​​at each node; The standardized value of the corresponding node indicator falls within the range of [0,1], and the larger the value, the higher the importance of risk transmission.

[0113] Handling of degradation scenarios: When the maximum value of a certain indicator equals the minimum value across all nodes (i.e., the range is zero), When the denominator of equation (10) is zero, the standardized value of the index on all nodes is uniformly set to zero, and the index does not participate in subsequent weighting; this convention also ensures that its overall discrimination is zero in step three, thus it is automatically removed. After step S2, each window obtains a OK Columns, elements The standardized value matrix of node indicators.

[0114] Step S3: Calculate the topological separation degree and index weights.

[0115] Step S3 calculates the overall discriminative power of each network topology indicator within each rolling time window based on the standardized values ​​of the node indicators across all product nodes, and calculates the head topology separation degree based on the difference between the top-ranked network topology indicators and the indicators of the remaining product nodes. The two are then combined and normalized to obtain the indicator weights of each network topology indicator within the rolling time window.

[0116] In step S3, calculating the overall discriminative power includes: converting the standardized values ​​of each node index corresponding to the same network topology index within the same rolling time window into node proportions; calculating the normalized information entropy based on each node proportion; and subtracting the normalized information entropy from 1 to obtain the overall discriminative power.

[0117] In step S3, calculating the head topology separation degree includes: determining the number of head product nodes according to a preset head ratio and the total number of product nodes, ensuring that the number of head product nodes is not less than 1 and less than the total number of product nodes; sorting the node index standardized values ​​from high to low, and determining the number of head product nodes at the top of the sorted list as the head product node set; calculating the index mean of the head product node set and the remaining product node sets respectively, and dividing the difference between the two index means by the non-zero range of the network topology index to obtain the head topology separation degree.

[0118] In step S3, the combined normalization of the two to obtain the indicator weights of each network topology indicator within the rolling time window includes: multiplying the overall distinguishability of the same network topology indicator within the same rolling time window by the head topology separation degree to obtain the original indicator weight score of the network topology indicator; dividing the original indicator weight score of each network topology indicator by the sum of the original indicator weight scores of all network topology indicators within the same rolling time window to obtain the indicator weight of each network topology indicator, and the sum of the indicator weights of all network topology indicators within the same rolling time window is 1; wherein, when either the overall distinguishability or the head topology separation degree is zero, the original indicator weight score of the corresponding network topology indicator is zero, and the network topology indicator does not participate in the weighted fusion of the window risk score. The specific content is as follows:

[0119] Step three involves the following steps: Within each rolling window, for each network topology metric, first calculate the overall discriminant based on the distribution of its standardized value across all nodes; then calculate the head topology separation based on the difference between the head node and the other nodes; finally, combine and normalize the two to obtain the metric weight. The overall discriminant answers the question "Does this metric differentiate across all nodes?", while the head topology separation answers "Can this metric significantly separate the most critical high-risk head nodes?" Both are indispensable.

[0120] (a) Calculation of overall discrimination.

[0121] The overall discrimination is constructed based on normalized information entropy and consists of three parts: node proportion, normalized information entropy, and discrimination.

[0122] 1. Node percentage.

[0123] Convert the standardized values ​​of each node corresponding to the same window and the same indicator into node proportions, that is, normalize the standardized values ​​to the share of the sum of all standardized values ​​of the indicator's nodes:

[0124] (11)

[0125] In equation (11): For the first Nodes in a window In the The percentage of nodes on each indicator meets the requirements. ; The standardized values ​​of the node indices in equation (10); A dummy index for summation across all nodes; denominator For the first Each indicator in all The sum of standardized values ​​at each node. Convention: A node with a standardized value of zero has a node percentage of zero, and the natural logarithm of zero multiplied by zero is zero; when the sum of standardized values ​​of an indicator is zero, the indicator is directly determined to be an indicator with no discrimination and no further calculation is performed.

[0126] 2. Normalized information entropy.

[0127] The normalized information entropy is calculated based on the proportion of each node to measure the uniformity of the distribution of this index value among the nodes.

[0128] (12)

[0129] In equation (12): For the first The first window The normalized information entropy of each indicator; ln is the natural logarithm. Based on the total number of nodes The normalization coefficient with base is such that the information entropy falls within the interval [0,1]. Let be the node proportion in equation (11). It is stipulated that when... When, the corresponding summation term Zero is taken (i.e., 0·ln0=0 is agreed upon) to eliminate numerical anomalies caused by taking the logarithm of zero. When the proportion of each node is nearly evenly distributed, the information entropy is close to 1, indicating that the index can hardly distinguish nodes; when the proportion is highly concentrated in a few nodes, the information entropy approaches 0.

[0130] 3. Overall distinguishability.

[0131] Subtracting the normalized information entropy from 1 yields the overall discriminative power, which changes in the same direction as the "discrepancy information content":

[0132] (13)

[0133] In equation (13): For the first The first window The overall distinguishability of each indicator, with a value range of [0,1]; Let be the normalized information entropy of equation (12). The greater the overall distinguishability, the more difference information the indicator provides among all product nodes and the stronger the overall dispersion; conversely, the smaller the overall distinguishability, the more similar the values ​​of each node are and the weaker the overall distinguishability of the indicator.

[0134] (ii) Calculation of head topological separation degree.

[0135] Overall discrimination alone is not enough to guarantee the indicator's ability to identify "high-risk head nodes". Therefore, a head topological separation degree is further constructed, which consists of four steps: determining the number of head nodes, grouping the head nodes, and normalizing the separation degree of the mean and range of the two groups.

[0136] 1. The number of nodes for the leading products is determined.

[0137] The number of head product nodes is determined according to the preset head ratio and the total number of product nodes, and a squeeze constraint is used to ensure that the number of head nodes is neither less than 1 nor strictly less than the total number of product nodes.

[0138] (14)

[0139] In equation (14): The number of nodes for the top products; Preset head proportions (0 < <1); The total number of product nodes; the inner max(1,·) ensures that the number of header nodes is at least 1, and the outer min( ,·) Ensure that the number of heads is at most This means that at least one "remaining node" is always retained, ensuring that header grouping holds true regardless of node size. For example, when , hour, This value is for illustrative purposes only and does not constitute a limitation.

[0140] 2. The head set is separated from the rest of the sets.

[0141] Under the same window and the same indicator, all nodes will be standardized according to the node indicator values. Sort in descending order from highest to lowest, and take the top-ranked items. These nodes constitute the head product node set. The remaining Nm nodes constitute the set of the remaining product nodes. The two constitute the entire A partition of the nth node. If the nth node... If there are parallel values, the parallelism can be broken by using a pre-fixed product node coding order, or all parallel nodes can be included in the header set and updated synchronously. When handling the same case, one of the parallel rules is always used, and the original sorting and subsequent resampling sorting also use the same deterministic parallel processing rule.

[0142] 3. Mean values ​​of the two sets of indicators.

[0143] Calculate the standardized mean values ​​of the head product node set and the remaining product node sets separately:

[0144] (15)

[0145] (16)

[0146] In equations (15) and (16): For the collection of top product nodes Inside The mean of the standardized values ​​of each node (the superscript T indicates the Top set). For the remaining product node set The mean of the standardized values ​​of the Nm nodes (the superscript R indicates the rest of the Rest set); , These are the aforementioned head set and the remaining sets, respectively. Equation (16) requires N>m, a condition guaranteed by the constraint of Equation (14); the head grouping is not executed when the number of nodes is insufficient. The head set is determined by descending order of the same window and the same index.

[0147] 4. Head topology separation degree with range normalization.

[0148] Dividing the difference between the head mean and the other means by the non-zero range of the index across all nodes yields a dimensionless, cross-index comparable head topological separation:

[0149] (17)

[0150] In equation (17): For the first The first window Head topological separation of each metric; molecule The denominator is the difference between the head mean and the rest mean; This represents the non-zero range of the indicator across all nodes, used to eliminate the influence of variations in the indicator's value range. Since the head set is obtained by sorting in descending order, the mean of the head set is not less than the mean of the others, and the numerator does not exceed the denominator. It is between 0 and 1; the indices without discrimination (range is zero) are not included in this formula. The larger the value, the more clearly the indicator can separate high-risk nodes from ordinary nodes. It should be noted that the italics appearing alone in equations (4) to (6)... This indicates the GFEVD prediction step size, and the subscripted value here... The two terms, representing the topological separation degree of the header, are distinguished by whether they include subscripts and the context, and have different meanings.

[0151] (III) Combination, normalization and generation of indicator weights.

[0152] The original indicator weight score is obtained by multiplying the overall discrimination score by the head topology separation score, and then normalized among all indicators in the same window to obtain the indicator weights that sum to 1.

[0153] 1. Original indicator weight scores.

[0154] (18)

[0155] In formula (18): For the first The first window The original indicator weight score of each indicator; The overall distinguishability of equation (13); Let be the head topological separation degree of equation (17). Using multiplicative combination means that any component approaching zero will significantly reduce the contribution of this indicator to the window risk score: only indicators that are discrete across all nodes and can significantly separate head nodes can obtain a high original score; when and When either of them is zero, The corresponding indicators are not included in the weighted fusion of window risk scores.

[0156] 2. Normalized index weights.

[0157] (19)

[0158] In equation (19): For the first The first window Normalized indicator weights for each indicator; The original index weight score of equation (18); denominator All in the same window The sum of the original scores of each indicator, where l is a dummy index for summing all indicators. After normalization, the sum of the indicator weights of all network topology indicators within the same scrolling window is 1, i.e. Degradation processing: When the sum of the weight scores of all original indicators in the same window is zero, the division operation is not performed, and the scrolling window is marked as an "invalid indicator window" for unified processing in step S6.

[0159] Step S4: Generate window risk scores and rankings.

[0160] Step S4 involves weighted fusion of standardized values ​​from multiple nodes within the same product node according to their respective weights, yielding the window risk score and window risk ranking for each product node within each rolling time window. Details are as follows:

[0161] The task of step S4 is to use the index weights obtained in step S3 to weight and fuse multiple standardized index values ​​of the same node within each window to obtain the window risk score of each node under that window, and generate the original window risk ranking accordingly, which serves as the benchmark sequence for subsequent resampling stability comparison.

[0162] No. Product nodes in each window The window risk score is its Each standardized indicator value is assigned a weight. Weighted sum:

[0163] (20)

[0164] In equation (20): For the first Product nodes in a scrolling window Window risk score; The normalized index weights of equation (19); The standardized values ​​of the node indices in equation (10); The number of indicators. Because... ∈[0,1] and Therefore ∈[0,1], a higher score indicates a higher importance of the node in the risk propagation within the current window. After obtaining the window risk scores for all nodes, according to... Sort by risk from highest to lowest to generate the original window risk ranking for this window. Parallel nodes are processed using a deterministic parallel processing rule that is completely consistent with the header set partitioning in step S3, to ensure that the sorting is unique and reproducible. Executing equation (20) window by window yields the window risk score sequence and the original window risk sorting sequence for all windows.

[0165] Step S5: Resample and reconstruct, and calculate window stability.

[0166] Step S5 performs multiple block resampling operations for each rolling time window. After each resampling, the directed weighted risk network is reconstructed, the network topology index, index weight, window risk score, and resampling risk ranking are recalculated, and the window resampling stability is calculated based on the rank correlation between the original window risk ranking and the multiple resampling risk rankings.

[0167] In step S5, the window resampling stability is the mean of the stability components corresponding to multiple effective resamplings; each stability component is obtained by interval mapping of the Kendall tau-b rank correlation coefficient between the original window risk ranking and the corresponding resampled risk ranking; the block resampling is either moving block resampling or cyclic block resampling, and the same time block index is used synchronously for the return sequences of all product nodes to preserve the local time-series correlation structure within the window and the contemporaneous relationship between product nodes. The specific details are as follows:

[0168] Step S5 aims to quantify the statistical reliability of the risk ranking obtained for each window: Multiple block resampling is performed on the window, with each resampling reconstructing the network from the return series and retracing the entire process of indicator calculation, weighting, and ranking. The window resampling stability is then calculated using the rank correlation between the original window risk ranking and the risk rankings from each resampling. Unlike approaches that only examine fluctuations in a single intermediate parameter, this step measures the stability of the entire process "from the original time series, network edge estimation, topology indicators, weighting, to node ranking."

[0169] (i) Block resampling method and time structure preservation.

[0170] Considering the local time-series autocorrelation in the return series and the contemporaneous correlation between product nodes, ordinary point-by-point independent random resampling would disrupt these two dependency structures. This invention employs block resampling, specifically moving block bootstrap or circular block bootstrap: first, the time series within the window is divided into several adjacent time blocks according to a preset block length; then, these time blocks are randomly sampled with replacement and concatenated end-to-end to ensure the resampled sequence length matches the original window. The block length is greater than 1 and less than the window sample size. An integer is used to preserve the local timing-dependent structure within the window.

[0171] Crucially, the same time block index (the same time block starting sequence and splicing order) is used synchronously for the yield sequences of all product nodes. This means that all nodes are sampled synchronously at the same time position in a single resampling, thus fully preserving the contemporaneous relationship between product nodes and avoiding time misalignment caused by independent resampling. The random seed, time block index, block length, and splicing order used in each resampling are all recorded to ensure recalculation.

[0172] (ii) Full-process reconstruction after resampling.

[0173] For each resampled return sequence obtained from block resampling, the processing chain from steps S1 to S4 is completely repeated: reorganize the return window, re-estimate the VAR model and perform Granger causality tests, regenerate the directed weighted risk network, recalculate and standardize all network topology indices, recalculate the overall discriminant and head topology separation, recalculate the index weights, recalculate the window risk score and generate the resampled risk ranking for this iteration. ,in The index is used to indicate the number of resampling attempts. If a resampling attempt fails to complete model estimation (e.g., the model does not converge) or fails to generate a valid window for the index, then that attempt is not counted in the valid resampling count and resampling is performed. If the number of valid resampling attempts still does not reach the preset minimum number of valid resampling attempts after the preset maximum number of attempts has been reached, the window is marked as an "invalid resampling window" and is left for processing in step S6.

[0174] (iii) Stability measures based on Kendall tau-b rank correlation.

[0175] For each valid resampling, calculate the original window risk ranking. Ranking by risk of this resampling The rank correlation coefficient between them. This invention uses the Kendall tau-b rank correlation coefficient, which can correctly handle parallel ordering, and its value range is [-1, 1]; then it is mapped to the [0, 1] interval by linear interval mapping (1+τ) / 2 to obtain the single stability component; the average value of the stability components of all effective resampling is taken to obtain the window resampling stability:

[0176] (twenty one)

[0177] In equation (21): For the first The window resampling stability of each rolling window has a value range of [0,1]. The closer it is to 1, the more stable the original sorting is under resampling perturbation and the more reliable the result is. For the first The actual number of effective resampling operations completed in each window; For valid resampling sequence numbers, ; The original window risk ranking obtained from equation (20); For the first The resampling risk ranking is obtained by resampling through full-process reconstruction. The Kendall-Tau-B rank correlation coefficient between the two sorts, with subscripts... This represents the tau-b version, with values ​​in the range [-1, 1]. The linear mapping [1+τ] / 2 takes the value 1 when τ=1 (completely identical sorting), 0 when τ=-1 (completely reversed sorting), and 0.5 when τ=0. The original sorting and the resampled sorting use the same deterministic parallel processing rules.

[0178] Step S6: Calculate the time proximity coefficient and window weight.

[0179] Step S6 calculates the time proximity coefficient based on the distance of each rolling time window from the latest rolling time window, combines the coefficient with the window resampling stability and normalizes it to obtain the window weight of each rolling time window.

[0180] In step S6, the time proximity coefficient decays exponentially according to the distance between the rolling time window and the latest rolling time window expressed in a unified time unit; the sum of the indicator weights within the same valid window is 1, and the sum of the window weights of all valid windows is 1; when the sum of the combined values ​​of the overall discriminative power and the head topology separation power of each network topology indicator within the same rolling time window is 0, the rolling time window is marked as an invalid indicator window; when the window resampling stability is lower than a preset stability threshold, the corresponding rolling time window is marked as a low-reliability window, and the weight of the rolling time window in the final risk score calculation is reduced.

[0181] In step S6, combining and normalizing the coefficients with the window resampling stability to obtain the window weights of each rolling time window includes: multiplying the time proximity coefficient of the same rolling time window with the window resampling stability to obtain the original window weight score of that rolling time window; setting a validity indicator value for each rolling time window, wherein the validity indicator value of rolling time windows marked as invalid indicator windows or invalid resampling windows is 0, and the validity indicator value of the remaining rolling time windows is 1; dividing the product of the original window weight score and its validity indicator value of each rolling time window by the sum of the products of the original window weight scores and their validity indicator values ​​of all rolling time windows to obtain the window weight of each rolling time window, and the sum of the window weights of all rolling time windows is 1. The specific content is as follows:

[0182] Step S6 involves performing a second layer of weighting along the window dimension: on the one hand, calculating the time proximity coefficient of exponential decay based on the distance of the window from the latest window; on the other hand, introducing the window resampling stability from step five. Combining these two factors with window effectiveness normalization results in window weights that sum to 1, thus making the "more recent and more stable" window contribute more to the final result.

[0183] (a) Time proximity coefficient.

[0184] A time proximity coefficient is calculated based on the distance of each scrolling window relative to the latest scrolling window, and it decays exponentially.

[0185] (twenty two)

[0186] In equation (22): For the first The time approximation coefficient for each scrolling window; For the first The distance between the current scrolling window and the latest scrolling window; The time decay parameter is non-negative. The larger the value, the faster the decay occurs for earlier windows; It is an exponential function with base e. Distance In a single case, a consistent approach must be adopted: either use the window sequence difference or use the actual time difference of the window endpoint expressed in a uniform time unit; these methods must not be mixed across different windows; the latest scrolling window... Therefore, its time proximity coefficient The earlier the window The bigger, The smaller.

[0187] (ii) Original window weight score.

[0188] Multiplying the temporal proximity coefficient of the same window by the window resampling stability yields the original window weight score, which simultaneously reflects temporal freshness and result reliability:

[0189] (twenty three)

[0190] In equation (23): For the first The original window weight score of each scroll window; The time proximity coefficient of equation (22); The window resampling stability of Equation (21) is determined by the multiplicative combination. Earlier windows or windows with unstable resampling will receive lower original scores, while only windows that are both recent and stable will receive higher scores.

[0191] (iii) Validity indicator value and normalized window weight.

[0192] Set a validity indicator value for each scrolling window, and uniformly remove invalid windows during normalization. Window weights are calculated using the following formula:

[0193] (twenty four)

[0194] In equation (24): For the first Normalized window weights for each scroll window; The original window weight score of equation (23); For the first The validity indicator value of each rolling window is either 0 or 1. The rolling window marked as an invalid indicator window (the denominator of equation (19) is zero) or an invalid resampling window (insufficient number of valid steps in step S5) takes 0, while the other normal windows take 1. This represents the total number of rolling time windows; A dummy index for summing across all windows. Numerator Automatically set the weight of invalid windows to zero, denominator This is the sum of the "validity × original score" of all windows. After normalization, the sum of the window weights of all valid windows is 1, i.e. (Invalid windows) =0).

[0195] (iv) Low reliability window and fallback rules.

[0196] In addition to invalid windows, a low-reliability window rule is also set: when window resampling stability When the value is below the preset stability threshold, the window is marked as a low reliability window and its weight in the final risk score calculation is reduced. A certain approach is to reset its window weight to zero and then normalize it again within the remaining valid windows. In Equation (19), "the sum of the combined values ​​of the overall discrimination of each indicator and the topological separation of the head in the same window is 0" corresponds to an invalid indicator window, and its validity indicator value is set to zero. Fallback rule: If the sum of the original window weight scores of all valid windows (i.e., the denominator of Equation (24)) is zero, then division is not performed, and only the window weight of the latest valid window is set to 1 and the weight of the remaining windows is set to 0, so as to ensure that the process always has a definite output.

[0197] Step S7: Output the set and sorting of high-risk product nodes.

[0198] Step S7 weights and fuses the window risk scores of the same product node across multiple windows according to window weights to obtain the final risk score, and outputs the set of high-risk product nodes and their ranking. Details are as follows:

[0199] The task of step S7 is to use the window weights from step S6 to weight and merge the window risk scores of the same product node across multiple windows into a final risk score, and then output the set of high-risk product nodes and their descending order according to the final score to complete the end-to-end identification.

[0200] (a) Final risk score for product nodes.

[0201] For each product node, assign a window risk score to it within each window. By window weight The weighted sum is used to obtain the final risk score:

[0202] (25)

[0203] In equation (25): For product nodes Final risk score for product nodes; outer layer For all Summing each window, For the window weights in equation (24), the invalid window's Therefore, it does not contribute; inner layer That is, the window risk score of formula (20) Therefore, equation (25) is equivalent to · ; The index weights in equation (19) are... The standardized value of equation (10) is given. This two-layer weighted structure ensures that only the "index-window" combination that simultaneously possesses topological identification capability (index layer), temporal validity, and resampling stability (window layer) will contribute significantly to the final score.

[0204] (ii) Output of high-risk product node set and sorting.

[0205] Product nodes are sorted from highest to lowest according to their final risk scores, and percentiles are determined based on a preset proportion of high-risk nodes. Nodes with scores reaching or exceeding a certain percentile are included in the high-risk product node set.

[0206] (26)

[0207] In equation (26): A set of nodes for high-risk products; The final risk score for equation (25); To pre-determine the proportion of high-risk nodes; The final risk score set for all nodes Experience distribution in The quantile (or percentile point) is used to determine the risk level. Nodes with a final score at or above this quantile are included in the high-risk set; if there are ties at a quantile, all tied nodes are included in the set. Alternatively, instead of using quantiles, a fixed number of nodes can be output based on a predetermined deterministic tie rule, ranking the nodes at the top. It is important to emphasize the proportion of high-risk nodes. Head proportions compared to equation (14) Independent and separately configured: This serves as the header grouping for assigning weights to indicators within a single window. The high-risk set selection serves the final result, and there is no binding relationship between the two.

[0208] (III) Results output and application methods.

[0209] The output should include at least: product node identifier, final risk score of the product node, current descending sort, and the contribution of each scrolling window to the node. · ) and the contribution of each network topology metric to the node ( (And its cross-window accumulation). The above results can be written into the risk monitoring database or used to generate a tiered early warning list, allowing risk managers to identify the high-risk nodes in the industry chain that require priority control. When all rolling windows are determined to be invalid, a "data insufficient" status is output instead of generating a high-risk node ranking to avoid outputting unreliable conclusions.

[0210] General boundary handling, parallel rules, and numerical verification:

[0211] To ensure that the method still has a definite and reproducible output under non-ideal conditions such as degraded data, model estimation failure, and unilateral ranking, this general method sets the following unified rules throughout steps S1 to S7.

[0212] (a) Indicator-level degradation rules.

[0213] When the range of a certain indicator across all nodes is zero (the denominator of equation (10) is zero), or the sum of its standardized values ​​is zero (the denominator of equation (11) is zero), the indicator is marked as an indicator without discrimination, its standardized values ​​are uniformly set to zero, and its overall discrimination is set to zero. Then, its original indicator weight score is determined by equation (18). It does not participate in the weighted fusion of window risk scores.

[0214] (ii) Window-level invalidity and low-reliability rules

[0215] When the sum of the weighted scores of all original indicators in a window is zero (the denominator of equation (19) is zero), the window is marked as an invalid indicator window; when the number of effective resampling attempts for a window is still less than the minimum number of effective attempts after reaching the maximum number of attempts, it is marked as an invalid resampling window; the validity indicator values ​​of the two types of invalid windows The window weight is determined by equation (24). This does not participate in the final score. When window resampling stability... When the data level falls below a preset stability threshold, it is marked as a low-reliability window, its weight is reset to zero, and it is renormalized within the remaining valid windows. When all windows are invalid, the output data is insufficient, and no high-risk node sorting is generated.

[0216] (III) Rules for parallel and catch-all arrangements

[0217] In Step 3 (head set division), Step 4 (original window risk sorting), Step 5 (resampling sorting), and Step 7 (high-risk set truncation), the same set of pre-fixed deterministic parallel processing rules are used for the parallel events that occur (breaking the parallel events according to the preset product node coding order, or including the parallel nodes as a whole and updating the quantity synchronously). One rule is used in the same case. When the denominator of Equation (24) is zero, only the weight of the latest valid window is set to 1; Equation (26) includes all parallel nodes at the quantile.

[0218] (iv) Reproducibility and numerical verification

[0219] All random block resampling saves the random seed, block length, target valid count, minimum valid count, and maximum number of attempts; the calculation configuration of all topology indicators is written to the configuration record and saved with the results to ensure that the results can be recalculated.

[0220] Example 2: Implementation of a high-risk node identification system for bulk commodity supply chains.

[0221] like Figure 3 As shown, Figure 3 This is a structural diagram of the high-risk node identification system for the bulk commodity supply chain of the present invention.

[0222] Figure 3 The system shown includes a dynamic network generation module, a topology index calculation module, an index weighting module, a window risk calculation module, a stability calculation module, a window weighting module, and a risk node output module. Each module can be implemented by a software functional unit executed by the same processor, or by multiple computing nodes in the order of data flow.

[0223] The dynamic network generation module outputs a window-by-window adjacency matrix; the topology index calculation module outputs standardized node index values; the index weighting module outputs index weights; the window risk calculation module outputs window risk scores and original window risk rankings; the stability calculation module outputs window resampling stability; the window weighting module outputs normalized window weights; and the risk node output module outputs a set and ranking of high-risk product nodes.

[0224] This invention also provides a high-risk node identification system for bulk commodity supply chains, applied in a computing device to implement the above-mentioned method. The system includes:

[0225] The dynamic network generation module is used to obtain the price time series of multiple product nodes in the commodity industry chain, divide multiple rolling time windows, generate corresponding directed weighted risk networks for each window, and obtain a dynamic directed weighted risk network sequence.

[0226] The topology metric calculation module is used to calculate multiple network topology metrics for each product node for each directed weighted risk network and perform unidirectional dimensionless transformation to obtain standardized node metric values.

[0227] The indicator weighting module is used to calculate the overall discrimination of each network topology indicator within each rolling time window based on the standardized value of the node indicator across all product nodes, and to calculate the head topology separation degree based on the difference between the top-ranked network topology indicator and the indicators of the remaining product nodes. The two are combined and normalized to obtain the indicator weight of each network topology indicator within the rolling time window.

[0228] The window risk calculation module is used to weight and fuse the standardized values ​​of multiple node indicators of the same product node according to the indicator weight, so as to obtain the window risk score and window risk ranking of each product node in each rolling time window;

[0229] The stability calculation module is used to perform multiple block resampling for each rolling time window. After each resampling, the directed weighted risk network is reconstructed, the network topology index, index weight, window risk score and resampling risk ranking are recalculated, and the window resampling stability is calculated based on the rank correlation between the original window risk ranking and the multiple resampling risk rankings.

[0230] The window weighting module is used to calculate the time proximity coefficient based on the distance of each scrolling time window from the latest scrolling time window, combine the coefficient with the window resampling stability and normalize it to obtain the window weight of each scrolling time window.

[0231] The system also includes a risk node output module, which is used to weight and fuse the window risk scores of the same product node in multiple windows according to window weights, obtain the final risk score, and output the set of high-risk product nodes and their ranking.

[0232] Example 3: Implementation of an electronic device.

[0233] This embodiment provides an electronic device for identifying high-risk nodes in a bulk commodity supply chain, including a processor, a memory, and a data communication interface. The memory stores a computer program executable by the processor. When the processor executes the computer program, it implements all the steps of the method for identifying high-risk nodes in a bulk commodity supply chain.

[0234] Specifically, the data communication interface is used to connect to an external price database or industry chain data platform to obtain the price time series of multiple product nodes in the commodity industry chain and transmit them to the processor. The processor loads and runs the computer program in the memory, and sequentially executes the complete process of rolling time window division, directed weighted risk network construction, multi-dimensional network topology index calculation and unidirectional standardization, dual-dimensional calculation of overall discrimination and head topology separation, index weight normalization, window risk scoring and sorting generation, block resampling and window resampling stability calculation, time proximity coefficient and window weight normalization, cross-window risk fusion, and output of high-risk product node set.

[0235] The electronic device described in this embodiment can be deployed independently in a commodity risk monitoring system and a supply chain risk control platform, or it can be embedded in a commodity trading management system and a market early warning system to provide stable and accurate support for identifying and ranking high-risk nodes for industry participants, financial institutions and regulatory authorities.

[0236] Example 4, an implementation of a computer-readable storage medium.

[0237] This embodiment provides a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, it implements all the steps of the method for identifying high-risk nodes in the commodity supply chain.

[0238] Specifically, the computer-readable storage medium is a non-transitory storage medium, which may be any one or more combinations of read-only memory (ROM), random access memory (RAM), magnetic storage medium (such as hard disk, floppy disk, magnetic tape), optical storage medium (such as read-only optical disc, digital multifunction optical disc), solid-state storage medium (such as flash memory, solid-state hard disk), etc., and does not include transient propagation media such as carrier signals.

[0239] When the computer program is loaded and run by the processor, it can sequentially execute the complete processing flow of price time series acquisition and preprocessing, rolling time window division, directed weighted risk network construction, multi-dimensional network topology index calculation and unidirectional standardization, dual-dimensional calculation of overall discrimination and head topology separation, index weight normalization, window risk scoring and ranking generation, block resampling and window resampling stability quantification, time proximity coefficient calculation and window weight normalization, cross-window risk fusion and output of high-risk product node set, and has a complete boundary anomaly handling and result verification mechanism.

[0240] The computer-readable storage medium described in this embodiment can be used for the software deployment, distribution, and offline upgrade of the commodity risk monitoring system, facilitating the delivery of the high-risk node identification method as a standardized software product to supply chain production enterprises, commodity trading institutions, financial institutions, and market regulatory departments.

[0241] Example 5, based on Example 1, demonstrates a specific application for identifying high-risk nodes in the bulk commodity supply chain.

[0242] 1. Generation of dynamic directed weighted risk network sequences.

[0243] In this embodiment, the computing device obtains price time series of multiple commodity product nodes arranged according to a unified time frequency from a price database or data interface. First, it checks the timestamps, duplicates, missing values, and zero or negative values ​​of the prices; only for prices that are strictly positive and have valid timestamps, the logarithmic return is calculated according to equation (1). The missing value imputation model only uses the corresponding rolling window endpoint and previous observations for fitting, prohibiting the use of data after the window endpoint to avoid future information leakage; each product node within the same window uses a unified time index. After unifying the unit of measurement, the data is calculated according to equation (2) with the window length... A rolling time window is formed with the preset step size.

[0244] Within each window, a VAR model is established according to equation (3), and the GFEVD contribution is calculated using equation (4). Since the first subscript of the standard GFEVD represents the receiving node and the second subscript represents the impulse source node, this embodiment stores the matrix uniformly as the first subscript according to equation (7). Line 1 The column represents the risk generated by the node. Pointing to node Then, the temporal causal screening matrix is ​​generated according to Equation (8), and the same-position product is performed according to Equation (9) to obtain the sparse directed weighted risk adjacency matrix of the window.

[0245] In other implementations, the directed weighted risk adjacency matrix for each rolling time window can be obtained directly from an external network generation device; as long as each window uses the same set of nodes, the same edge direction convention, and comparable edge weight definitions, the subsequent two-layer weighting steps can be executed.

[0246] Second: Weighting of indicators based on overall distinguishability and head topology separation.

[0247] For each window, calculate at least three of the following: weighted outward strength, weighted inward strength, weighted betweenness centrality, risk propagation PageRank, weighted k-core, and local weighted clustering coefficients of the node. Weighted outward strength is the sum of the weights of all non-self-looping outward edges of the node, and weighted inward strength is the sum of the weights of all non-self-looping inward edges of the node. When calculating weighted betweenness centrality, positive edge weights are converted to propagation distances, which are the reciprocals of the edge weights. Distances without edges are taken as infinity, and then summed according to the proportion of the number of shortest paths passing through the node to the total number of corresponding shortest paths. Risk propagation PageRank uses directed edge weights to normalize the transition probability, with a damping coefficient set to a fixed value greater than 0 and less than 1. The probability quality of nodes without outward edges is evenly distributed to all nodes. Weighted k-core uses the same preset weighted kernel decomposition rule, maintaining the definitions of strength, degree, and stripping threshold unchanged across all windows and all resampling. The local weighted clustering coefficients of nodes adopt the same preset directed weighted triangle closure rule, and the weight normalization and directed triangle type remain unchanged across all windows and all resampling. The above calculation configuration is written to the configuration record and saved along with the recognition results to ensure comparability of results from different windows and resampling.

[0248] Standardize each indicator according to the same-direction range using equation (10). If the maximum and minimum values ​​of an indicator are the same across all nodes, set all standardized values ​​of that indicator to zero, and the overall discrimination will be zero in the subsequent calculation. Calculate the overall discrimination according to equations (11) to (13).

[0249] The number of head nodes is determined according to equation (14). The head set and the remaining node sets are formed in descending order of index values. Then, the head topology separation degree is calculated according to equations (15) to (17). If the first... If there are parallel values, the parallelism can be broken by using a pre-fixed product node coding order, or all parallel nodes can be included in the header set and updated synchronously. A single rule is consistently applied when handling the same case.

[0250] The original indicator weight scores are calculated according to Equation (18) and normalized according to Equation (19). The indicator only receives a higher weight when both the overall discrimination and the head topology separation are high. The window risk score is obtained according to Equation (20) and the original window risk ranking is formed.

[0251] 3. Window weighting based on temporal proximity and resampling stability.

[0252] Calculate the time proximity coefficient according to formula (22). Within a single case, the window sequence number difference or the actual time difference of the window endpoint expressed in a uniform time unit should be used consistently; it must not be mixed between different windows; time decay parameter. It is a non-negative number. A larger value indicates faster decay for earlier windows. If you want the time proximity factor to decrease to half its original value after half a life of h1 / 2, you can set it as follows: =ln2 / h1 / 2, where h1 / 2 uses the same unit as the window distance.

[0253] For each window, perform either moving block resampling or cyclic block resampling. The block length lb is greater than 1 and less than the window sample size. The integer; all product nodes are synchronized using the same set of time block start points and splicing order to ensure that the synchronization relationship between nodes is not misaligned due to resampling. After each resampling, the yield window organization, VAR and Granger model estimation, risk network generation, network topology indicator calculation, overall discrimination calculation, head topology separation calculation, indicator weight calculation, and node risk ranking are re-executed. If a resampling fails to complete model estimation or generate an effective indicator window, that resampling is not counted as a valid resampling count. And resample; windows that have not reached the preset minimum number of valid resampling attempts after reaching the preset maximum number of attempts are marked as invalid resampling windows.

[0254] The window resampling stability is calculated according to Equation (21). In this embodiment, the Kendalltau-b rank correlation coefficient, which can handle parallel ranking, is used; each time the correlation coefficient is linearly mapped from negative 1 to 1 to 0 to 1, and then the mean of the Bt valid results is calculated. The original ranking and the resampling ranking use the same deterministic parallel processing rules. The original window weight score is calculated according to Equation (23), and then the normalized window weights with a sum strictly equal to 1 are obtained within the set of valid windows using Equation (24).

[0255] 4. Final scoring, boundary handling, and numerical verification.

[0256] Calculate the final risk score for each product node according to equation (25), and output the set of high-risk product nodes and sort them in descending order according to equation (26) or a preset number of nodes. The proportion of high-risk nodes in equation (26) is also considered. Head proportions compared to equation (14) Configure separately; when quantile points are tied, all tied nodes will be included in the high-risk product node set. The output results include product node identifier, final risk score, current ranking, contribution of each window, and contribution of each network topology indicator, which can be written to the risk monitoring database or used to generate a graded early warning list.

[0257] When the range of an indicator across all nodes is zero or the sum of its standardized values ​​is zero, the indicator is marked as an indicator with no discriminative power, and its original indicator weight score is set to zero. When the sum of the original indicator weight scores for a window is zero, the window is marked as an invalid indicator window and does not participate in the final scoring; when all windows are invalid, the output is a data insufficiency status and no high-risk node ranking is generated. When a window resampling is invalid, it is excluded from the set of valid windows; when the window resampling stability is lower than a preset stability threshold, it can be marked as a low-reliability window, and its window weight is reset to zero before being renormalized within the remaining valid windows. If the sum of the original scores of valid windows is zero, only the window weight of the latest valid window is set to 1. Random resampling should save the random seed, block length, target valid count, minimum valid count, and maximum number of attempts to ensure recalculation.

[0258] In the numerical verification example, assuming the original weight scores of two indicators for a certain window are 0.2 and 0.3 respectively, the normalized indicator weights are 0.4 and 0.6 respectively; and the two standardized indicator values ​​for a certain node are 0.8 and 0.5 respectively, then the window risk score is 0.62. If the original window weight scores of the three windows are 0.3, 0.5, and 0.8, then the window weights are 0.1875, 0.3125, and 0.5 respectively; when the risk scores of the three windows for this node are 0.4, 0.6, and 0.8, the final risk score is 0.6625. The above values ​​are only used to verify the formula chain and do not limit the scope of the claims.

[0259] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention in any way. 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.

[0260] The above embodiments are merely illustrative examples and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A method for identifying high-risk nodes in a bulk commodity supply chain, characterized in that, Performed by a computing device, including: S1. Obtain the price time series of multiple product nodes in the commodity industry chain, divide multiple rolling time windows, generate corresponding directed weighted risk networks for each window, and obtain a dynamic directed weighted risk network sequence. S2, for each directed weighted risk network, calculate multiple network topology indicators for each product node and perform unidirectional dimensionless transformation to obtain standardized values ​​of node indicators. S3. For each network topology indicator within each rolling time window, calculate the overall discrimination based on the distribution of the standardized values ​​of the node indicators across all product nodes, and calculate the head topology separation based on the difference between the top-ranked network topology indicators and the indicators of the remaining product nodes. Combine and normalize the two to obtain the indicator weights of each network topology indicator within the rolling time window. S4, weighted and fused the standardized values ​​of multiple node indicators for the same product node according to the indicator weight, to obtain the window risk score and window risk ranking of each product node in each rolling time window; S5, perform multiple block resampling for each rolling time window, reconstruct the directed weighted risk network after each resampling, recalculate the network topology index, index weight, window risk score and resampling risk ranking, and calculate the window resampling stability based on the rank correlation between the original window risk ranking and the multiple resampling risk rankings. S6. Calculate the time proximity coefficient based on the distance of each rolling time window from the latest rolling time window, combine the coefficient with the window resampling stability and normalize it to obtain the window weight of each rolling time window. S7: Weighted fusion of window risk scores for the same product node across multiple windows according to window weights to obtain the final risk score, and output the set of high-risk product nodes and their ranking.

2. The method for identifying high-risk nodes in a bulk commodity supply chain according to claim 1, characterized in that, In step S1, the step of generating the corresponding directed weighted risk network window by window includes: calculating the logarithmic return series for strictly positive price time series; establishing a vector autoregressive model for the return series within each rolling time window, and generating a directional spillover matrix based on the generalized prediction error variance decomposition; performing Granger causality tests on ordered product node pairs to generate a time-series causality screening matrix; performing a co-position product operation on the directional spillover matrix and the time-series causality screening matrix, setting the edge weights of directional spillover edges that fail the Granger causality test to zero, and setting the weights of self-loop edges to zero, thereby obtaining the directed weighted risk network.

3. The method for identifying high-risk nodes in a bulk commodity supply chain according to claim 1, characterized in that, In step S2, the multiple network topology indicators include at least three of the following: weighted outgoing strength, weighted incoming strength, weighted betweenness centrality, risk propagation PageRank, weighted k-core, and node local weighted clustering coefficient; wherein, all network topology indicators are set such that the larger the value, the higher the importance of risk propagation of the product node.

4. The method for identifying high-risk nodes in a bulk commodity supply chain according to claim 1, characterized in that, In step S3, calculating the overall discriminative power includes: converting the standardized values ​​of each node index corresponding to the same network topology index within the same rolling time window into node proportions; calculating the normalized information entropy based on each node proportion; and subtracting the normalized information entropy from 1 to obtain the overall discriminative power.

5. The method for identifying high-risk nodes in a bulk commodity supply chain according to claim 1, characterized in that, In step S3, calculating the head topology separation degree includes: determining the number of head product nodes according to a preset head ratio and the total number of product nodes, ensuring that the number of head product nodes is not less than 1 and less than the total number of product nodes; sorting the node index standardized values ​​from high to low, and determining the number of head product nodes at the top of the sorted list as the head product node set; calculating the index mean of the head product node set and the remaining product node sets respectively, and dividing the difference between the two index means by the non-zero range of the network topology index to obtain the head topology separation degree.

6. The method for identifying high-risk nodes in a bulk commodity supply chain according to claim 1, characterized in that, In step S3, the combination and normalization of the two to obtain the index weights of each network topology index within the rolling time window includes: multiplying the overall distinguishability of the same network topology index within the same rolling time window by the head topology separation degree to obtain the original index weight score of the network topology index; dividing the original index weight score of each network topology index by the sum of the original index weight scores of all network topology indices within the same rolling time window to obtain the index weight of each network topology index, and the sum of the index weights of all network topology indices within the same rolling time window is 1; wherein, when either the overall distinguishability or the head topology separation degree is zero, the original index weight score of the corresponding network topology index is zero, and the network topology index does not participate in the weighted fusion of the window risk score.

7. The method for identifying high-risk nodes in a bulk commodity supply chain according to claim 1, characterized in that, In step S5, the window resampling stability is the average of the stability components corresponding to multiple effective resamplings; Each stability component is obtained by interval mapping of the Kendall tau-b rank correlation coefficient between the original window risk ranking and the corresponding resampled risk ranking; the block resampling is either moving block resampling or cyclic block resampling, and the same time block index is used synchronously for the return series of all product nodes to preserve the local time-series correlation structure within the window and the contemporaneous relationship between product nodes.

8. The method for identifying high-risk nodes in a bulk commodity supply chain according to claim 1, characterized in that, In step S6, the time proximity coefficient decays exponentially according to the distance between the rolling time window and the latest rolling time window expressed in a unified time unit; the sum of the indicator weights within the same valid window is 1, and the sum of the window weights of all valid windows is 1; when the sum of the combined values ​​of the overall discriminative power and the head topology separation power of each network topology indicator within the same rolling time window is 0, the rolling time window is marked as an invalid indicator window; when the window resampling stability is lower than a preset stability threshold, the corresponding rolling time window is marked as a low-reliability window, and the weight of the rolling time window in the final risk score calculation is reduced.

9. The method for identifying high-risk nodes in a bulk commodity supply chain according to claim 1, characterized in that, In step S6, combining and normalizing the coefficients with the window resampling stability to obtain the window weights of each rolling time window includes: multiplying the time proximity coefficient of the same rolling time window with the window resampling stability to obtain the original window weight score of that rolling time window; setting a validity indicator value for each rolling time window, wherein the validity indicator value of the rolling time window marked as an invalid indicator window or an invalid resampling window is 0, and the validity indicator value of the remaining rolling time windows is 1; dividing the product of the original window weight score and its validity indicator value of each rolling time window by the sum of the products of the original window weight score and its validity indicator value of all rolling time windows to obtain the window weight of each rolling time window, and the sum of the window weights of all rolling time windows is 1.

10. A high-risk node identification system for a bulk commodity supply chain, applied in a computing device, for implementing the method according to any one of claims 1-9, characterized in that the system... include: The dynamic network generation module is used to obtain the price time series of multiple product nodes in the commodity industry chain, divide multiple rolling time windows, generate corresponding directed weighted risk networks for each window, and obtain a dynamic directed weighted risk network sequence. The topology metric calculation module is used to calculate multiple network topology metrics for each product node for each directed weighted risk network and perform unidirectional dimensionless transformation to obtain standardized node metric values. The indicator weighting module is used to calculate the overall discrimination of each network topology indicator within each rolling time window based on the standardized value of the node indicator across all product nodes, and to calculate the head topology separation degree based on the difference between the top-ranked network topology indicator and the indicators of the remaining product nodes. The two are combined and normalized to obtain the indicator weight of each network topology indicator within the rolling time window. The window risk calculation module is used to weight and fuse the standardized values ​​of multiple node indicators of the same product node according to the indicator weight, so as to obtain the window risk score and window risk ranking of each product node in each rolling time window; The stability calculation module is used to perform multiple block resampling for each rolling time window. After each resampling, the directed weighted risk network is reconstructed, the network topology index, index weight, window risk score and resampling risk ranking are recalculated, and the window resampling stability is calculated based on the rank correlation between the original window risk ranking and the multiple resampling risk rankings. The window weighting module is used to calculate the time proximity coefficient based on the distance of each scrolling time window from the latest scrolling time window, combine the coefficient with the window resampling stability and normalize it to obtain the window weight of each scrolling time window. The system also includes a risk node output module, which is used to weight and fuse the window risk scores of the same product node in multiple windows according to window weights, obtain the final risk score, and output the set of high-risk product nodes and their ranking.

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