Water diversion project risk cascade propagation and risk assessment method and system based on multi-level topology structure

Abstract

This invention discloses a method and system for risk cascading propagation and risk assessment of water transfer projects based on a multi-level topology. The method includes: acquiring the topology network of the water transfer project; generating a node comprehensive risk vector for each node based on multi-source operational data; constructing a basic risk propagation matrix based on physical connections; structurally modulating the node comprehensive risk vectors to generate a comprehensive propagation operator; performing cascading propagation iterative evolution of the node comprehensive risk vectors based on the comprehensive propagation operator, and continuously calculating the network dynamics stability characteristic parameter of the comprehensive propagation operator during the evolution process; when the system is determined to be in a divergent phase based on this parameter, reconstructing the comprehensive propagation operator and continuing iterative evolution until convergence to obtain a steady-state risk distribution; and outputting the system comprehensive risk assessment result based on the steady-state risk distribution. This invention can improve the operational safety management capability of water transfer projects under complex operating conditions and external disturbances.

Description

Technical Field

[0001] This invention relates to the field of water conservancy project operation safety assurance and technical assessment, and in particular to a method and system for risk cascading propagation and risk assessment of water transfer projects based on multi-level topology. Background Technology

[0002] Water transfer projects involve complex topological relationships across multiple levels, including main lines, branch lines, and tributaries. These relationships involve deep nonlinear spatiotemporal coupling between structural states, operational deviations, and external environmental disturbances. Accurately characterizing the cross-level transmission mechanisms of multi-source risk factors among heterogeneous engineering units and establishing a dynamic evolutionary model with algebraic convergence is of significant technical value for predicting large-scale topological stability of long-distance water transfer systems and for adaptive feedback control of operational conditions.

[0003] Existing technologies for risk assessment of water diversion networks mainly employ single-node static evaluation models or linear cascade models based on fixed weights. These schemes typically pre-configure an unchanging risk propagation matrix, calculate a comprehensive risk index through bottom-up data aggregation, and trigger static alarms or assess the security level of local units based on preset constant thresholds within a unidirectional information flow framework.

[0004] The aforementioned static evaluation methods suffer from deep-seated technical defects such as unclosed propagation mechanisms, unclear phase transition boundaries, and lack of physical attenuation constraints, which can lead to dynamic distortion or numerical divergence in evaluation results under complex operating conditions. Specifically, existing constant threshold models struggle to respond to the erosion of system carrying capacity by strong external disturbances. Furthermore, their use of fixed propagation weights fails to map the macroscopic situation at different levels back to local nodes, lacking the ability to characterize nonlinear transitions with multi-scale bidirectional coupling. They also lack explicit modeling of the engineering hierarchy, failing to establish bidirectional coupling between nodes and levels, making it difficult to reflect the impact of the overall situation on local risk propagation. Due to the absence of theoretical constraints on spatial physical attenuation factors and network spectral radius eigenvalues, traditional linear iterative evolution equations cannot guarantee convergence, making it difficult for the model to define the divergence and convergence phase boundaries of risk propagation from an algebraic perspective. They also fail to construct a cascading propagation model of risk in the topology, making it difficult to characterize the diffusion trend of risk over time. In addition, static models lack an adaptive reconstruction mechanism that proactively intervenes and truncates propagation weights based on phase determination results. Once local extreme degradation occurs, the original model is prone to generating negative weights or physical fallacies of reverse propagation, making it difficult to accurately reflect the reshaping feedback process of network dynamics structure by engineering disaster prevention and control intervention. In other words, the lack of a system-wide stability determination mechanism makes it difficult to determine whether the risk is in a decaying or spreading state. In emergency dispatch or structural state change scenarios, existing technologies struggle to accurately describe the dynamic evolution of risk from local anomalies to system-wide changes. Summary of the Invention

[0005] The purpose of this invention is to provide a method and system for risk cascading propagation and risk assessment in water diversion projects based on multi-level topology, in order to solve at least one of the aforementioned problems in the prior art.

[0006] According to one aspect of this application, a method for risk cascading propagation and risk assessment in water diversion projects based on multi-level topology includes:

[0007] Obtain the topology network of the water transfer project based on the structure of the main line, the water outlet and the branch line, and generate the node comprehensive risk vector of each node based on the multi-source project operation data;

[0008] A basic risk propagation matrix is ​​constructed based on the physical connections in the topology network of the water diversion project, and a comprehensive propagation operator is generated by structurally modulating the basic risk propagation matrix based on the node comprehensive risk vector.

[0009] The node comprehensive risk vector is cascaded and iteratively evolved based on the comprehensive propagation operator. During the evolution process, the network dynamic stability characteristic parameters of the comprehensive propagation operator are continuously calculated to determine the system phase.

[0010] When the system is determined to be in a divergent phase state based on the network dynamics stability characteristic parameters, an adaptive triggering reconstruction operation is performed on the integrated propagation operator to reduce the propagation intensity of the integrated propagation operator, generating a reconstructed integrated propagation operator. Based on the reconstructed integrated propagation operator, cascade propagation iterative evolution is continued until convergence, obtaining the steady-state risk distribution and the network propagation topology characteristics during the evolution process.

[0011] Based on the steady-state risk distribution and combined with the network propagation topology characteristics, the system's comprehensive risk assessment results are output.

[0012] According to another aspect of this application, a risk cascading propagation and risk assessment system for water diversion projects based on a multi-level topology includes:

[0013] Memory, used to store computer programs;

[0014] A processor is used to execute a computer program to implement the steps described in any one of the above-mentioned methods for risk cascading propagation and risk assessment of water diversion projects based on multi-level topology.

[0015] Beneficial effects: This invention effectively avoids the numerical divergence of traditional linear models, realizes the leap from water diversion projects to nonlinear dynamic reconfiguration closed-loop system evaluation, risk propagation path identification, risk assessment and system stability determination, and can improve the safety management and control capabilities of water diversion projects under complex operating conditions and external disturbances. Attached Figure Description

[0016] Figure 1This is a schematic diagram of a method for risk cascading propagation and risk assessment of water diversion projects based on a multi-level topology, provided in an embodiment of this application.

[0017] Figure 2 This is a schematic diagram of the process of generating a comprehensive propagation operator by performing nonlinear enhancement modulation on the coupled propagation matrix based on the node comprehensive risk vector provided in this application embodiment.

[0018] Figure 3 This is a schematic diagram of the process of obtaining the reconstructed comprehensive propagation operator by reducing the propagation intensity of the comprehensive propagation operator through adaptive triggering reconstruction operation provided in the embodiments of this application.

[0019] Figure 4 This is a schematic diagram of the positive value truncation mechanism for preventing negative propagation weights provided in the embodiments of this application. Detailed Implementation

[0020] This invention divides engineering nodes based on the trunk-branch-tributary structure and constructs a hierarchical directed topology; it collects information such as structural status, operating conditions, control reliability, and external disturbances to calculate the comprehensive risk value of each node; it constructs a risk propagation matrix and introduces a multi-scale coupling modulation and threshold enhancement mechanism to realize the cascading propagation calculation of risk in the engineering topology; it determines the stable state of system risk through the spectral radius of the propagation matrix and dynamically reconstructs the propagation structure in critical or diffusion states; finally, it outputs the system risk level and scheduling control recommendations. The implementation process is described in detail below through examples.

[0021] Example 1 provides an overall flowchart for a risk cascading propagation and risk assessment method for water diversion projects based on a multi-level topology, such as... Figure 1 As shown, this paper elaborates on the closed-loop risk assessment system and basic operation framework of the entire process in water transfer projects, from data acquisition, operator modulation, cascade evolution to dynamic reconstruction and result output.

[0022] Step 101: Obtain the topology network of the water diversion project based on the structure of the main line, the water outlet and the branch line, and generate the node comprehensive risk vector of each node based on the multi-source project operation data.

[0023] Specifically, when acquiring the topology network of a water diversion project, the project area is divided into a set of nodes whose risks can be independently assessed based on their physical structure and water flow logic. Nodes corresponding to main lines can be physical structures such as canal sections, tunnels, inverted siphons, aqueducts, or pumping stations. Nodes corresponding to branch lines mainly include branch gates, metering facilities, and control and communication units. Nodes corresponding to branch lines are channel projects that receive water from branch lines and transport water downstream. Directed connections are established between nodes based on water flow direction and control logic, forming a water diversion project topology network that reflects the interrelationships between the project entities.

[0024] Furthermore, the process of generating a node-wide comprehensive risk vector requires deep integration of multi-dimensional monitoring and inspection data. Specifically, the multi-source engineering operation data is analyzed into four risk assessment components: a structural state risk factor characterizing the degree of anomalies in the structure itself and the foundation; an operational deviation risk factor characterizing the degree of deviation of the actual scheduling from the target interval; a control reliability risk factor characterizing the decline in control link and equipment support capabilities; and an external disturbance factor characterizing the driving effect of the external environment.

[0025] In the specific implementation, normal and severe thresholds are pre-set for each type of risk factor. A conventional piecewise linear mapping function is used to convert the collected raw monitoring values ​​into normalized anomaly scores. These four scores are then weighted linearly and combined according to preset weights for structure, operation, control, and external groups to calculate the node's comprehensive risk value for the current assessment period. The node's comprehensive risk values ​​for all nodes are arranged in topological order to form the node's comprehensive risk vector.

[0026] In some alternative implementations, when the predetermined node lacks real-time online monitoring data, manual inspection records or historical fault statistics frequency can be used as proxy indicators to calculate the degree of anomaly, so as to ensure the data integrity of the node's comprehensive risk vector in the spatial dimension.

[0027] Step 102: Construct a basic risk propagation matrix based on the physical connection relationships in the topology network of the water diversion project, and perform structured modulation on the basic risk propagation matrix based on the node comprehensive risk vector to generate a comprehensive propagation operator.

[0028] A basic risk propagation matrix was constructed to quantify the initial impact strength between node risks. Specifically, a basic propagation weight was assigned to each directed edge in the water diversion project's topology network. The basic propagation weight was obtained by multiplying four physical evaluation factors: structural coupling strength, operational coupling degree, target node importance, and data reliability. Among them, structural coupling strength was assigned based on the tightness of physical connections, such as adjacent trunk lines or cross-layer control; operational coupling degree was calculated by the ratio of current flow to design flow; target node importance was determined according to the project level; and data reliability was downgraded based on the proportion of sensor missing measurement time.

[0029] A static basic risk propagation matrix is ​​insufficient to reflect the sudden changes in risk and the hierarchical amplification effect under extreme conditions, necessitating structured modulation. This modulation process uses the macroscopic overall risk situation at the hierarchical level and the microscopic local high-risk state of nodes as feedback signals. Through mathematical methods such as matrix multiplication and nonlinear mapping, the edge weights in the basic risk propagation matrix are adaptively amplified or redistributed to obtain a comprehensive propagation operator that can truly drive the dynamic evolution.

[0030] In some alternative implementations, in order to reduce computational complexity, under normal operating conditions and without significant external disturbances, the amplification factor of the structured modulation can be set to a unit value by default. In this case, the integrated propagation operator degenerates into the basic risk propagation matrix.

[0031] Step 103: Based on the comprehensive propagation operator, the node comprehensive risk vector is subjected to cascade propagation iterative evolution. During the evolution process, the network dynamic stability characteristic parameter of the comprehensive propagation operator is continuously calculated to determine the system phase. When the system is determined to be in a divergent phase based on the network dynamic stability characteristic parameter, an adaptive triggering reconstruction operation is performed on the comprehensive propagation operator to reduce the propagation intensity of the comprehensive propagation operator and generate a reconstructed comprehensive propagation operator. Based on the reconstructed comprehensive propagation operator, the cascade propagation iterative evolution continues until convergence, and the steady-state risk distribution and the network propagation topology characteristics during the evolution process are obtained.

[0032] This step can also specifically involve constructing an actual evolutionary propagation operator based on the comprehensive propagation operator, and performing cascaded propagation and iterative evolution of the node comprehensive risk vector based on the actual evolutionary propagation operator. During the evolution process, the network dynamic stability characteristic parameters of the actual evolutionary propagation operator are continuously calculated to determine the system phase.

[0033] When the system is determined to be in a divergent phase based on the network dynamics stability characteristic parameters, an adaptive triggering reconstruction operation is performed on the integrated propagation operator to reduce the propagation intensity of the integrated propagation operator and generate a reconstructed integrated propagation operator. Based on the reconstructed integrated propagation operator, a reconstructed actual evolution propagation operator is constructed, and based on the reconstructed actual evolution propagation operator, cascaded propagation iterative evolution is continued until convergence, to obtain the steady-state risk distribution and the network propagation topology characteristics during the evolution process.

[0034] Specifically, the cascaded propagation iterative evolution is a discrete dynamic evolution process, with its initial state being the node comprehensive risk vector. In each iteration, the current risk state vector is multiplied using the actual evolutionary propagation operator to simulate the multi-order transmission and amplification effects of risk in the network structure. To determine whether the amplification effect is controllable, the system needs to monitor the network dynamic stability characteristic parameters in real time. These parameters, acting as mathematical stability discriminators, can rigorously indicate whether the current propagation operator will lead to an unlimited increase in network-wide risk.

[0035] When the system detects that the stability characteristic parameter exceeds the safety threshold, i.e., the system enters a divergent phase that is difficult to converge naturally, traditional static evaluation methods often fail, while this system actively intervenes. The automatically triggered reconstruction operation at this time is an adaptive control mechanism to prevent physical distortion. By forcibly suppressing excessively high weights in the propagation operator, eliminating secondary propagation edges, or reshaping the propagation channels of key nodes, the overall energy of the propagation matrix decreases, generating a reconstructed comprehensive propagation operator.

[0036] The system replaces the old integrated propagation operator with a dangerous state with a reconstructed integrated propagation operator, and constructs a reconstructed actual evolution propagation operator based on the reconstructed integrated propagation operator, continuing the original iterative process. Since the reconstructed operator has restored its mathematical convergence property, the increment of the risk vector will tend to zero after a finite number of iterations, eventually stabilizing in an invariant vector space. The numerical distribution in this space is the steady-state risk distribution.

[0037] Furthermore, when performing cascading propagation iterative evolution, a maximum number of iterations or a residual tolerance threshold can be set. When the difference in risk vector change between two adjacent iterations is less than the residual tolerance threshold, the iteration can be terminated early, and the system can be determined to have reached convergence.

[0038] Step 104: Based on the steady-state risk distribution and combined with the network propagation topology characteristics, output the comprehensive risk assessment results of the system.

[0039] In this embodiment, the steady-state risk distribution reflects the final risk-bearing level of each node after cascading propagation reaches equilibrium. The network propagation topology features record the dominant path of risk transmission and phase transitions during the evolution process. The dominant propagation path is determined by searching the directed chain with the largest product of the weights in the evolution operator. The phase transitions specifically include the sequence of phase types experienced by the system during evolution and the corresponding spectral radius values. The system extracts the average steady-state risk value of the entire network, the peak risk of the most dangerous node, and the cumulative strength of the dominant propagation chain, and integrates them into a dimensionless comprehensive scoring index.

[0040] Based on the numerical range of this comprehensive scoring index, the current engineering safety status is mapped to a preset risk level. For example, the risk level can be divided into four levels: low risk, medium risk, high risk, and extremely high risk. The final system comprehensive risk assessment result not only includes the above risk level identifiers, but can also directly output intervention command parameters for weak nodes such as flow limiting scheduling, enhanced inspection, or activation of backup facilities, realizing a complete closed loop from risk quantification to business response.

[0041] Optionally, the system's comprehensive risk assessment results can also be rendered and displayed on the front-end 3D engineering topology map through a visualization interface, in the form of a heat map or dynamic flow diagram, to help dispatchers quickly locate high-risk paths.

[0042] According to another aspect of this application, a risk cascading propagation and risk assessment system for water diversion projects based on a multi-level topology is provided, comprising:

[0043] A memory for storing computer programs; a processor for executing computer programs to implement the steps of any one of the methods described in the "Risk Cascading Propagation and Risk Assessment Method for Water Diversion Projects Based on Multi-Level Topology".

[0044] Example 2 elaborates on the physical constituent factors of the basic risk propagation matrix, the algebraic construction logic of the multi-scale bidirectional mapping operator, and the adaptive truncation update mechanism of scale coupling strength.

[0045] Step 201: Use the pre-constructed node-hierarchy bidirectional mapping relationship to perform multi-scale coupling modulation on the basic risk propagation matrix to obtain the coupled propagation matrix.

[0046] Before performing multi-scale coupled modulation, the system first needs to construct a basic risk propagation matrix. This matrix quantifies the initial inherent strength of risk transmission between engineering nodes in the water diversion project's topology network. Specifically, the basic propagation weight of each directed edge in the matrix is ​​determined by a combination of four physical factors, and its linear calculation formula is as follows:

[0047] w ij =S ij *O ij *I j *C ij ;

[0048] In this application, the propagation matrix uses a notation where columns represent source nodes and rows represent target nodes. ij This represents the propagation weight of risk from source node i to target node j; therefore, when the propagation matrix is ​​multiplied by the diagonal enhancement matrix on the right, the weight of all outgoing edges from source node i is amplified.

[0049] In the formula, w ij S is the basic propagation weight in the basic risk propagation matrix, pointing from source node i to target node j. ij For structural coupling strength, O ij To determine the degree of coupling, I j C represents the importance of the target node. ij To assess data credibility.

[0050] Specifically, structural coupling strength reflects the tightness of physical connections, with higher values ​​for connections between adjacent trunk nodes and intermediate values ​​for connections between control nodes spanning different levels. Operational coupling is calculated based on engineering fluid dynamics characteristics, specifically reflected as the ratio of the current real-time monitored flow rate to the design rated flow rate. Target node importance is normalized based on the target node's design level or water supply function priority within the water transfer network. Data reliability penalizes uncertainties caused by missing monitoring data; when a related node experiences sensor anomalies or missing measurements, the system reduces the value of this factor according to the proportion of the missing measurement duration to the total evaluation period. This product-type formula structure ensures that a high-intensity initial risk propagation channel is activated only when the physical structure is connected, the hydraulic conditions are active, and the monitoring data is valid.

[0051] Since the basic risk propagation matrix is ​​a static, local weighted perspective, it is difficult to characterize the amplification effect of the overall degradation of the pipeline network on the propagation capability of local single points. Therefore, the system must use a predefined algebraic mapping rule to perform structural up-dimensional modulation of its spatial dimension.

[0052] Step 202: Obtain the network-wide average risk value for the current assessment period, calculate the deviation between the network-wide average risk value and the pre-configured reference risk level, and extract the intensity update increment based on the deviation.

[0053] In constructing the bidirectional mapping relationship, the key parameter determining the feedback strength of the overall hierarchical situation to the local nodes is the scale coupling strength parameter. To endow the model with dynamic adaptability to hydrological characteristics at different operational stages, this parameter is not a fixed constant but rather evolves adaptively with the overall network's macroscopic security status. The system extracts the arithmetic mean of the comprehensive risk values ​​of all nodes in the current network as the average risk value for the entire network and compares it numerically with a pre-set normalized water network security benchmark.

[0054] Δγ=ε*(R avg -R ref );

[0055] Where Δγ is the intensity update increment; ε is the preset update learning rate, used to control the step size of the risk state change during the iterative update process, and its value is a preset small positive number, set according to the system convergence characteristics or historical data experience; R avg R represents the average risk value across the entire network. ref This is a pre-configured reference risk level.

[0056] In this embodiment, when the average risk value of the entire network is higher than the reference risk level, the system determines that the water network is in an overall deterioration trend. At this time, the extracted intensity update increment is positive, further intensifying the positive feedback coupling strength across scales. Conversely, when the risk of the entire network falls below the normal baseline, the extracted intensity update increment is negative, guiding the coupling effect between levels to slowly decline.

[0057] Step 203: The intensity update increment is superimposed onto the scale coupling intensity parameter of the previous evaluation period or the pre-configured initial scale coupling intensity parameter, and the superimposed result is truncated using the pre-configured upper and lower bounds of the intensity to generate the target scale coupling intensity parameter corresponding to the current evaluation period.

[0058] To prevent the system from being in a high-risk state for a long time due to external disturbances, causing the scale coupling strength parameter to monotonically increase to infinity and triggering the numerical divergence error of the dynamic evolution operator, it is necessary to implement hard boundary constraints to intercept the intermediate results after superposition and accumulation.

[0059] γ target =clip(γ prev +Δγ,γ min ,γ max );

[0060] Where, γ target γ is the coupling strength parameter at the target scale. prev The scale coupling strength parameter is from the previous evaluation period, Δγ is the strength update increment, and γ is the intensity parameter. min As a pre-configured lower bound for intensity, γ max The upper bound of the pre-configured intensity is defined by `clip`, which is the interval truncation function.

[0061] Specifically, the lower bound of the intensity is set to zero to ensure that the physical direction of the feedback modulation maintains positive logic and does not reverse. The upper bound of the intensity is calibrated based on the network layer thickness and basic weight level of the water diversion project, and is set as an empirically tolerated upper limit within the range of positive real numbers. Through the above-mentioned data processing mechanism with bounded truncation, it can be ensured that the generated target-scale coupling intensity parameters are always constrained within a closed interval with engineering physical significance.

[0062] Step 204: Based on the pre-constructed aggregation operator for characterizing the mapping from node to hierarchy and the feedback operator for characterizing the mapping from hierarchy to node, and combined with the pre-configured scale coupling strength parameter, construct a multi-scale modulation matrix.

[0063] Multi-scale modulation matrices are crucial mathematical operators for inversely modulating the overall operational status of a hierarchical system to individual local nodes. The system pre-establishes aggregation and feedback operators based on the hierarchical relationships within the water diversion project's network. The aggregation operator, a matrix structure, aggregates the risk values ​​of various dispersed nodes into a global evaluation index for its respective management level. The feedback operator, also a configuration matrix, remaps the calculated global evaluation index back to each lower-level engineering node within that hierarchy.

[0064] M=I'+γ*Ψ*Φ;

[0065] Where M is the multi-scale modulation matrix, I' is the identity matrix (notation with apostrophe is used here to distinguish it from other letter variables, and it is unrelated to the matrix transpose symbol), γ is the scale coupling strength parameter, Ψ is the feedback operator, and Φ is the aggregation operator.

[0066] Specifically, the matrix multiplication of the feedback operator and the aggregation operator forms a block constant matrix. Within this block constant matrix, nodes belonging to the same engineering level have non-zero constant values ​​for their corresponding row and column intersection elements, while nodes belonging to different levels have zero values ​​for their corresponding elements. This algebraic construction virtually creates horizontal same-layer coupling channels in the physical network, allowing isolated nodes within the same layer to share the macroscopic risk pressure of their respective level.

[0067] In some optional implementations, the element values ​​of the aggregation operator can be flexibly reconfigured according to the water supply security strategy. Under the default average aggregation mechanism, the element value at the corresponding position of a node in the same layer is the reciprocal of the total number of nodes in that layer, thus reflecting the average risk baseline of the layer. Furthermore, in monitoring scenarios involving major supply security tasks or highly sensitive sections, this can be smoothly replaced with a maximum value aggregation mechanism. In this case, the element value at the node position with the highest initial risk value in the corresponding layer is 1, and the element values ​​at the other nodes in the same layer are 0. This alternative mechanism can enhance the network operator's ability to capture and respond to extreme risks at local single points.

[0068] Step 205: Replace the pre-configured scale coupling strength parameter with the target scale coupling strength parameter to construct a multi-scale modulation matrix.

[0069] The target scale coupling strength parameters, which have undergone truncation and security verification in step 203, are substituted into the linear construction formula of the multi-scale modulation matrix described above. Through rolling parameter replacement over time, a logical closed loop from low-level situational feedback to high-level operator model updates is completed, ensuring that each generated matrix model fits the dynamic characteristics of network vulnerability in the current period.

[0070] Step 206: Multiply the multi-scale modulation matrix with the basic risk propagation matrix to obtain the coupled propagation matrix.

[0071] W Θ =M*W0; where W Θ Let M be the coupling propagation matrix, M be the multi-scale modulation matrix, and W0 be the basic risk propagation matrix.

[0072] Specifically, the system utilizes a left-multiplication linear operation to directly apply the multi-scale modulation matrix to the basic risk propagation matrix. The multi-scale modulation matrix acts on the basic risk propagation matrix from the left, representing the overall modulation of propagation relationships by the hierarchical overall situation. This left-multiplication operation, based on the original entity transmission path weights, weights and mixes the propagation relationships related to the corresponding level, thus reflecting the overall impact of macro-level risk pressure on the propagation relationships between nodes. When the overall water conveyance situation of a certain local subsystem fluctuates significantly, the propagation relationships related to that level will receive a corresponding modulation increment. This matrix transformation process, in the mathematical model, reproduces the nonlinear positive feedback phenomenon in engineering practice where the deterioration of local risks leads to an increase in system-level vulnerability.

[0073] Step 207: Perform nonlinear enhancement modulation on the coupled propagation matrix based on the node integrated risk vector to generate the integrated propagation operator.

[0074] After completing multi-scale matrix upscaling modulation in the spatial dimension, the coupling propagation matrix possesses the fundamental capability to handle hierarchical macroscopic correlation effects. In this state, the system further introduces a threshold-driven mechanism based on the safety status of micro-nodes. By real-time screening of the node comprehensive risk vector to identify extremely degraded nodes that have breached the safety threshold, and by applying a step-like nonlinear amplification factor to the local outgoing edge propagation weights of high-risk source nodes, a comprehensive propagation operator that balances macroscopic feedback and microscopic mutations is output. The specific details of how external perturbations drive nonlinear enhancement modulation will be explained in subsequent embodiments.

[0075] Example 3 details the mathematical model based on the dynamic pressure trigger threshold of system-level external disturbance indicators, and the specific technical processing steps for the hierarchical nonlinear amplification of out-of-limit weights, such as... Figure 2 As shown.

[0076] Step 301: Based on the real-time acquired external disturbance factors of each node and the node comprehensive risk vector, a weighted calculation is performed to obtain the system-level external disturbance index. The external disturbance factors are determined based on the environmental monitoring data of the location of each node collected in real time.

[0077] Specifically, the external disturbance factor is used to characterize the environmental stress level experienced by the engineering entity during the current assessment period. Rainfall intensity, seismic parameters, or regional deformation data at each node location are collected in real time and standardized and mapped to a predetermined numerical range to generate the external disturbance factor. Because the water diversion project extends in a strip-like pattern, the external disturbances encountered by each node often exhibit spatial heterogeneity. To comprehensively evaluate the environmental severity of the entire network at a macroscopic level, the system does not use a simple arithmetic average but instead utilizes the node comprehensive risk vector as a weighting coefficient for weighted fusion.

[0078] R e_sys =∑(R i *R e,i ) / ∑(R i );

[0079] Among them, R e_sys R represents the system-level external disturbance index, ∑ represents the summation operation over all nodes in the network, and R is the system-level external disturbance index. i R represents the overall node risk value for the corresponding node in the current network. e,i This refers to the external disturbance factor acquired in real time for the corresponding node.

[0080] Through the above calculation logic, external disturbances to high-risk nodes will have a more significant impact on system-level indicators. This mechanism aligns with the "barrel effect" principle in hydraulic engineering, where the entire pipeline system should exhibit greater sensitivity to sudden environmental changes when critical nodes in a structurally weak state encounter extreme weather or geological stress.

[0081] In some optional implementations, in order to prevent calculation anomalies where the denominator is zero under a secure network state, a very small positive real number can be superimposed on the summation result of the denominator as a numerical protection item to ensure the continuity and stability of the weighted operation.

[0082] Step 302: Use system-level external disturbance indicators to down-modulate the preset reference threshold to determine the dynamic trigger threshold.

[0083] In traditional cascading failure network models, a fixed constant is typically set as the critical trigger point for risk outbreak. However, this static mechanism ignores the erosive effect of the external environment on the engineering load-bearing limit. This embodiment introduces an external environment intervention mechanism, using calculated system-level external disturbance indices to directly change the system's trigger sensitivity. The more severe the external environment, the lower the system's tolerance for risk.

[0084] R crit =max(R crit_min ,R crit_0 -δ*R e_sys );

[0085] Among them, R crit The threshold is dynamically triggered, and max is the maximum value extraction function. R crit_min R is the pre-configured lower bound of the threshold. crit_0 The preset reference threshold is δ, which is the pre-configured external disturbance modulation coefficient, and R is... e_sys This is a system-level external disturbance indicator.

[0086] Specifically, the system linearly scales the system-level external disturbance index using external disturbance modulation coefficients and deducts it as a penalty from a preset baseline threshold, achieving threshold down-modulation. To prevent this dynamic trigger threshold from being reduced to zero or even becoming negative under extreme weather conditions, a maximum value extraction function is forcibly introduced for truncation protection. The pre-configured lower bound of the threshold can be set to 0.10, ensuring that even under the most extreme external disturbance conditions, a certain degree of substantial risk accumulation must exist to trigger the subsequent amplification mechanism, avoiding the logical fallacy of the model unconditionally activating the augmentation state.

[0087] Step 303: Extract the nodes that exceed the limit in the node comprehensive risk vector that are greater than or equal to the dynamic trigger threshold, and determine the graded enhancement coefficient based on the risk amplitude of the nodes that exceed the limit.

[0088] The system iterates through the node-wide risk vector, comparing the current risk magnitude of each node with the dynamic trigger threshold calculated in the previous step. Nodes that reach or exceed this threshold are marked as over-limit nodes. This indicates that the accumulated potential energy within the node has exceeded the safety envelope under the current environmental conditions, and its negative impact will no longer be limited to the local area but will have the potential to spill over outwards.

[0089] To accurately characterize the nonlinear features of the spillover effect, the system does not employ a single amplification ratio, but rather constructs a stepped mapping rule. Specifically, based on the numerical range within which the risk amplitude of an out-of-limit node falls, a corresponding graded enhancement coefficient is matched. For example, when the node risk amplitude just exceeds the dynamic trigger threshold and is less than 0.60, the corresponding graded enhancement coefficient can be set to 1.5; when the node risk amplitude is between 0.60 and 0.75, the graded enhancement coefficient climbs to 2.0; when the node risk amplitude is between 0.75 and 0.90, the graded enhancement coefficient further climbs to 2.5; when the node risk amplitude exceeds the critical threshold of 0.90, the graded enhancement coefficient reaches a peak of 3.0. Normal nodes not marked as out of limit have their corresponding enhancement coefficient strictly maintained at a unit value of 1.0.

[0090] Furthermore, in an alternative implementation, to avoid discontinuous oscillations caused by grade transitions in numerical calculations, the mechanism for determining the grade enhancement coefficient can be replaced with an exponential, continuously smooth activation function with the node risk amplitude as the independent variable, thereby achieving a smooth transition in enhancement intensity.

[0091] Step 304: Use the hierarchical enhancement coefficient to amplify the outgoing edge weights of the corresponding overlimit nodes in the coupling propagation matrix to generate the comprehensive propagation operator.

[0092] After obtaining the enhancement coefficients of all nodes in the network, a diagonal enhancement matrix is ​​constructed with the enhancement coefficients of each node as the principal diagonal elements. This diagonal enhancement matrix is ​​then right-multiplied by the coupling propagation matrix to obtain the comprehensive propagation operator.

[0093] W nl =W Θ *Λ; where W nl For the synthesis propagation operator, Λ is the diagonal enhancement matrix composed of hierarchical enhancement coefficients, and W is the propagation matrix. Θ This is the coupling propagation matrix. Through right multiplication, the outgoing edge weights of the corresponding nodes are amplified as a whole by their enhancement coefficients, thereby strengthening the driving effect of high-risk nodes on the propagation of system risk. Since the propagation matrix in this application represents the source nodes column-wise, right multiplication by the diagonal enhancement matrix is ​​equivalent to amplifying the column vectors of the corresponding source nodes as a whole, thus achieving synchronous enhancement of all their outgoing edge weights.

[0094] In the physical sense of matrix multiplication, this operation is equivalent to accurately locking the starting column vectors of all corresponding over-limit nodes in the network topology, and directly amplifying the propagation weights of all outgoing edges from the source node to its directly adjacent downstream nodes using the corresponding hierarchical enhancement coefficients. This transforms the microscopic crisis of local nodes into a reduction in the macroscopic transmission resistance of the network structure, reproducing the phase transition process in water diversion projects where local breaches or equipment failures trigger a chain reaction in the surrounding area. The resulting integrated propagation operator combines the three physical effects of infrastructure connectivity, multi-scale environmental positive feedback, and microscopic over-limit explosion amplification, providing an accurate computational basis for the rigorous dynamic iterative evolution in subsequent steps.

[0095] Example 4 elaborates on the dynamic mechanism of overcoming the cascade evolution divergence fallacy by introducing a space physics attenuation factor, the stability phase determination criterion based on spectral radius, and the unified evolution equation for cross-period state transition.

[0096] Step 401: Obtain the preset space-physical attenuation factor, scale the integrated propagation operator based on the space-physical attenuation factor, and construct the actual evolution propagation operator.

[0097] In traditional risk propagation network models, if unconstrained operators are used directly for iteration, risk energy often exhibits unbounded physical divergence due to the existence of loops. To rigorously guarantee the convergence of the cascade propagation dynamics system and give it a true physical meaning, this embodiment introduces a spatial physical attenuation factor. The spatial physical attenuation factor characterizes the natural attenuation law of risk influence as it propagates step-by-step along the engineering topology path; that is, the farther away from the source node, the weaker its direct contribution to the target node.

[0098] W prop =(1-μ d )*W nl Among them, W prop For the actual evolutionary propagation operator, μ d W is the preset spatial physical attenuation factor. nl For the comprehensive propagation operator.

[0099] Specifically, the system constructs a scaling scalar using a spatial physics attenuation factor and applies it directly to the integrated propagation operator generated in the aforementioned embodiments. The actual evolutionary propagation operator constructed through the scaling operation ensures that the risk attenuates by a fixed proportion each time it propagates across nodes. In engineering practice, the value of the spatial physics attenuation factor can be calibrated based on the measured attenuation data of a predetermined water diversion project, and a reasonable empirical range is suggested to be between 0.05 and 0.30. For example, a value of 0.1 indicates that the destructive impact of the risk will naturally decrease by 10% for each order of topological propagation.

[0100] Step 402: Using the node integrated risk vector as the initial iteration state, perform bounded truncation fixed-point iteration using the actual evolution propagation operator.

[0101] After obtaining the actual evolution and propagation operators, the system can initiate the core dynamic evolution process describing the multi-tiered transmission effect of risks. The node comprehensive risk vector generated in the current assessment cycle is used as the initial iterative state of the evolution starting point, and the actual evolution and propagation operators are repeatedly applied within discrete time steps to simulate the spread of hidden dangers from near to far in the pipeline network.

[0102] R (k+1) =clip(R(t)+W prop *R (k) ,0,1);

[0103] Among them, R (k+1) Let W be the risk state vector for the (k+1)th iteration, clip be the cutoff function, R(t) be the comprehensive risk vector for the current assessment period, and W be the risk vector for the (k+1)th iteration. prop For the actual evolution propagation operator, R (k) Let be the risk state vector for the k-th iteration.

[0104] Specifically, each iteration is equivalent to evaluating the cumulative effect of risk moving one step forward in the network. Since the accumulated risk values ​​of local nodes may overflow and lose physical meaning in extreme cases or dense topology networks, the system enforces a bounded, truncated fixed-point iteration format. The bounding operation strictly limits the single-step iteration result of each node to a closed normalized interval of [0,1], preventing numerical divergence from becoming uncontrollable.

[0105] Furthermore, under the ideal linear propagation condition that ignores the bounds truncation, the analytical expansion of this fixed-point iterative process is equivalent to the summation of a Neumann series. Since a physical attenuation mechanism has been introduced in the preliminary steps, this infinite series will inevitably converge absolutely, provided the predetermined mathematical conditions are met. The final risk borne by each node equals its inherent initial risk, plus the first-order propagation contribution from its directly connected neighbors after one attenuation, plus the sum of second-order and even higher-order diminishing contributions. This progressively decreasing mechanism ensures that the total amplification effect of the system is bounded.

[0106] In some alternative implementations, the termination condition for the iteration can be set to the difference between the infinite norms of the vectors in two adjacent iterations being less than a preset convergence tolerance, such as one ten-thousandth, or directly reaching a preset maximum number of iterations to meet the real-time computing requirements of the system.

[0107] Step 403: The network dynamic stability characteristic parameter is the spectral radius; continuously calculate the network dynamic stability characteristic parameter of the synthesized propagation operator, including: extracting the maximum eigenvalue modulus of the synthesized propagation operator to obtain the spectral radius.

[0108] Specifically, the maximum eigenvalue modulus of the integrated propagation operator is extracted first, and then the spectral radius of the actual evolutionary propagation operator is calculated by combining the space physics attenuation factor.

[0109] To make a priori quantitative prediction of the convergence trend of the aforementioned iterative evolution process at a macroscopic level, the system continuously calculates stability characteristic parameters that reflect the inherent properties of network topological dynamics. In this embodiment, this characteristic parameter is specifically defined as the spectral radius in mathematical analysis theory. Since the actual evolutionary propagation operator is a non-negative real matrix before deducting the attenuation factor, according to the Perron-Frobenius theorem, its spectral radius is strictly equal to the largest of the absolute values ​​of all complex eigenvalues ​​of this matrix, i.e., the Perron root.

[0110] ρ actual =(1-μ d )*ρ(W nl ); where ρ actualμ is the global spectral radius corresponding to the actual evolutionary propagation operator. d ρ(W) is a preset spatial physical attenuation factor. nl ) is the comprehensive propagation operator W nl The spectral radius is the modulus of the largest eigenvalue.

[0111] Using standard numerical algebraic algorithms, such as the power method or direct eigenvalue decomposition, the actual evolutionary propagation operator is analyzed for eigenvalues, and its maximum eigenvalue modulus is extracted to obtain the spectral radius. In an equivalent implementation, the synthesized propagation operator can also be analyzed for eigenvalues ​​first, and then the spectral radius of the actual evolutionary propagation operator can be obtained by combining the spatial physics attenuation factor. This index accurately characterizes the limiting ability of connected loops in a network to amplify small perturbations from a global perspective, and is a core variable that determines whether the aforementioned Neumann series can converge.

[0112] In the subsequent phase determination stage, the global spectral radius ρ of the actual evolution propagation operator can be directly used. actual By comparing it with the stability critical value of 1, the spectral radius ρ(W) of the synthesized propagation operator can also be equivalently expressed. nl The two determination paths are mathematically equivalent when compared with the stability threshold adjusted by the space physics attenuation factor.

[0113] Step 404: Compare the spectral radius with the preset stability critical value and the preset tolerance parameter.

[0114] After obtaining the spectral radius, the system uses it as a metric for phase transitions and compares it numerically with a pre-defined reference boundary in real time. The preset stability threshold is theoretically typically set to 1, representing the absolute equilibrium point where the cascade amplification effect reverses from decay to expansion. Simultaneously, considering the white noise interference and uncertainties caused by minor disturbances in the monitoring data during practical engineering, a preset tolerance parameter is introduced to construct a phase transition buffer band with a certain width. An empirically recommended value for the tolerance parameter is 0.05, ensuring that the critical judgment condition is not overly sensitive and frequently triggers false alarms.

[0115] Step 405: When the spectral radius is greater than the sum of the stability critical value and the tolerance parameter, the system is determined to be in a divergent phase.

[0116] Based on this comparison, the system established a strict criterion for determining the three-phase dynamics. When the spectral radius is strictly less than the difference between the stability critical value and the tolerance parameter, it is determined to be in a convergent phase. At this time, the fixed-point iteration exhibits compression mapping characteristics, the cascade propagation effect decays step by step, and the system possesses inherent stability to resist local sudden high-risk risks. When the spectral radius is between the critical value minus the tolerance parameter and the critical value plus the tolerance parameter, the system is determined to be in a critical phase. At this time, the iterative convergence is relatively slow, and small disturbances can easily cause instability, indicating that management needs to increase the level of monitoring attention.

[0117] Once the calculation reveals that the spectral radius exceeds the upper limit (i.e., is greater than the sum of the stability critical value and the tolerance parameter), it is decisively determined to be in a divergent phase. Physically, this determination indicates that the cascading propagation effect has broken free from the constraints of natural attrition. The risk increment at remote engineering nodes not only fails to diminish with increasing distance but instead exhibits a catastrophic increasing trend with each step amplifying. This determination will serve as the highest priority control signal, directly triggering subsequent adaptive reconstruction and hard network intervention targeting the propagation operator.

[0118] Step 406: Obtain the initial inherent risk vector for the next cycle.

[0119] For water diversion projects implementing continuous rolling monitoring, risk assessment cannot be limited to a single, isolated time slice. To ensure the system can accurately reflect the evolution trajectory of risk over a longer time scale, this embodiment introduces a cross-cycle state transition and update mechanism after a single-cycle assessment. When the system enters the next predetermined assessment cycle, the front-end sensor network and data fusion module will recalculate and obtain the initial inherent risk vector representing the latest engineering status based on the latest measured engineering data.

[0120] Step 407: Based on the preset fusion coefficient of new and old data, the initial inherent risk vector of the current period and the initial inherent risk vector collected in the next period are linearly mixed to obtain the transitional risk state.

[0121] Because the deterioration of engineering structures or the spread of potential hazards often exhibit a time-dependent memory effect, risks inherited from the previous assessment cycle should not be simply discarded. The system introduces a pre-set data fusion coefficient to reconcile the proportional relationship between historically accumulated risks and the most recently collected risks.

[0122] R trans (t+1)=(1-λ e )*R(t)+λ e *R new (t+1);

[0123] Among them, R trans (t+1) represents the transitional risk state, λe Let R(t) be the preset fusion coefficient between the old and new data, and R(t) be the initial inherent risk vector for the current period. new (t+1) is the initial inherent risk vector collected in the next cycle, and t is the evaluation cycle index.

[0124] Through the above linear interpolation hybrid operation, the system obtains a transitional risk state that connects the past and the future. In some optional implementations, the fusion coefficient of the old and new data can be set to 0.6, indicating that during the state update process, the system tends to accept the latest measured risk characteristics, which account for 60%, while retaining the initial inherent risk of the previous cycle, which accounts for 40%, as a momentum smoothing buffer.

[0125] Step 408: Construct a cascaded amplification inverse matrix based on the actual evolution propagation operator, and use the cascaded amplification inverse matrix to perform mapping transformation and bounded truncation processing on the transition risk state to obtain the cross-period state transition update result containing the multi-order amplification effect of the historical network.

[0126] In order to make the cross-cycle evolution not only include the numerical smoothing of a single node, but also reflect the systematic amplification ability of the entire network topology to hidden dangers, a unified evolution equation including global cascading effects is constructed.

[0127] R(t+1)=clip(M inv *R trans (t+1),0,1);

[0128] Where R(t+1) is the cross-cycle state transition update result including the multi-order amplification effect of the historical network, clip is the bounded truncation processing function, and M inv R is the inverse matrix of the cascaded amplification. trans (t+1) represents the transitional risk state.

[0129] Specifically, the cascaded amplification inverse matrix is ​​mathematically expressed as the inverse of the difference between the identity matrix and the actual evolutionary propagation operator. Dynamically, the inverse matrix structure is equivalent to the network-wide amplification effect after the convergence of infinitely many cascaded propagation iterations in the preceding steps. The system uses this cascaded amplification inverse matrix to perform a spatial dimension mapping transformation on the aforementioned transitional risk states generated by the hybrid process. To prevent numerical anomalies caused by excessively high amplification factors at individual nodes, a bounded truncation of the [0, 1] closed interval is applied again, ultimately outputting a rigorously closed cross-period state transition update result. This closed-loop equation realizes the complete analytical path of the water diversion network from time updates to spatial cascaded mapping.

[0130] Example 5 elaborates on the multi-element triggering mechanism, three-step serial execution logic, and nonlinear physical truncation model for the adaptive reconstruction operation to reverse divergent phase states.

[0131] Step 501, the adaptive triggering reconfiguration operation is triggered not only when the system is determined to be in a divergent phase, but also when at least one of the following conditions is met: the maximum node risk amplitude is extracted from the node comprehensive risk vector, and the maximum node risk amplitude is triggered when it is greater than the preset node risk warning threshold; based on the real-time acquired system-level external disturbance index, the system-level external disturbance index is triggered when it is greater than the preset external disturbance critical threshold.

[0132] In the complex operating environment of water diversion projects, the outbreak of risks exhibits multi-dimensional warning signs. Relying solely on spectral radius as the sole criterion often results in a lag. Therefore, the system establishes a logical OR gate triggering mechanism encompassing three dimensions. The first dimension is the instability of the global network structure, corresponding to the spectral radius exceeding the critical boundary and entering a divergent phase. The second dimension focuses on microscopic ontological security, extracting extreme nodes with high risk levels within the current assessment period. A preset node risk warning threshold can be set at 0.85, indicating that even if the overall network has not yet formed widespread cascading divergence, as long as the severity of a single node's hidden danger approaches the red line for project destruction, pre-emptive reconstruction measures must be taken. The third dimension departs from the internal topology and shifts to a feedforward response to macroscopic environmental pressures. A preset external disturbance critical threshold can be set at 0.70. When encountering extreme rainstorms or strong earthquakes that cause environmental indicators to surge, reconstruction operations can be initiated directly to enhance the network's defensive posture without waiting for substantial damage to the internal structure.

[0133] Step 502: Adaptively trigger the reconstruction operation to reduce the propagation strength of the synthesis propagation operator to obtain the reconstructed synthesis propagation operator, such as... Figure 3 As shown, the process includes: performing hierarchical propagation suppression processing on the comprehensive propagation operator to reduce the propagation weights corresponding to high-risk levels; performing node risk-oriented reinforcement processing on the propagation operator after hierarchical propagation suppression processing based on the node comprehensive risk vector to enhance the incoming edge weights corresponding to high-risk nodes; and performing edge structure pruning processing on the propagation operator after node risk-oriented reinforcement processing using a preset pruning threshold to reset the propagation weights less than the pruning threshold to zero, thereby generating a reconstructed comprehensive propagation operator.

[0134] To eliminate algebraic ambiguities and physical conflicts arising from the parallel superposition of multiple reconstruction strategies, this embodiment adopts a three-step serial execution logic. The reconstruction operation is a dynamic transformation process with a specific sequence. The system first approaches the problem from a macroscopic level, performing hierarchical propagation suppression processing. By significantly reducing the spillover effects of high-risk layers, the overall propagation energy of the network is rapidly reduced. Based on this initially suppressed intermediate-state operator, the system transitions to microscopic targeted operations, performing node risk-oriented reinforcement processing. This step does not change the total energy of the propagation matrix; instead, it increases the sensitivity of high-risk nodes to receiving external signals, forcing subsequent iterative evaluation results to impose a greater penalty bias on weak links. Following this, edge structure pruning is implemented. The preset pruning threshold can be set to 0.01, cutting off and setting to 0 weak propagation edges whose weights are below this threshold after the first two rounds of modulation. This operation not only eliminates redundant edges that contribute minimally to the cascading effect and reduces the iterative computational overhead of large networks, but also ultimately solidifies the generated reconstruction comprehensive propagation operator.

[0135] Among them, the inhibition coefficient α at each level l During pre-calibration, levels exhibiting higher overall risk levels or stronger amplification characteristics in historical risk propagation are assigned a larger α value. l The value of α is chosen to provide stronger suppression in the divergent phase state, thus demonstrating a preferential suppression effect on high-risk levels in terms of mechanism; for low-risk levels or levels with low propagation amplification characteristics, α... l Choose a smaller value to maintain appropriate propagation capability. α l The specific value can be determined through offline calibration based on the importance level of the project hierarchy and historical risk data, or the same value can be uniformly selected to achieve uniform suppression across all levels.

[0136] Step 503, during the hierarchical propagation suppression process, specifically includes a positive value truncation mechanism to prevent propagation weights from taking negative values: Based on the deviation magnitude of the network dynamics stability characteristic parameters and a preset suppression coefficient, an initial hierarchical suppression factor is calculated; the initial hierarchical suppression factor is compared with the maximum value of the preset lower bound of the suppression factor, and the maximum value is extracted as the target hierarchical suppression factor; the propagation weights at high-risk levels are reduced using the target hierarchical suppression factor, such as... Figure 4 As shown in the figure. Specifically, the deviation magnitude refers to the positive deviation of the network dynamics stability characteristic parameter from the stability critical value.

[0137] In some embodiments, the initial hierarchical suppression factor can be calculated based on the deviation of the dominant factor that triggers the reconstruction operation, such as the deviation of network dynamic stability characteristic parameters or the excess magnitude of external disturbance characteristics, and a preset suppression coefficient.

[0138] In traditional linear control theory, simply multiplying the deviation amplitude by a coefficient for negative feedback regulation can easily cause the adjusted proportional coefficient to fall below zero when the deviation amplitude is too large. Therefore, a positive value truncation mechanism based on maximum value comparison is introduced.

[0139] η layer,l =max(η min ,1-α l *ρ dev );

[0140] Where, η layer,l η is the target level suppression factor; max is the maximum value extraction function; η min The lower bound of the preset inhibitory factor; α l The preset inhibition coefficient is used to characterize the intensity of the inhibition effect of level l in the risk propagation process. Its value can be determined according to the importance of different levels or historical data; ρ dev This represents the deviation magnitude of the network dynamics stability characteristic parameter, i.e., the positive deviation.

[0141] After determining the target level suppression factor for each level, a level reduction matrix D is constructed with the level suppression factor of each node as its diagonal element. layer D layer [i,i]=η layer,l(i) Let l(i) represent the level to which node i belongs. Perform a right multiplication operation W on the synthesis propagation operator. (l) =W nl *D layer This reduces the weights of all outgoing edges from each source node proportionally according to the suppression factor of its respective level. Since the propagation matrix in this application uses column notation for source nodes, the right multiplication operation is equivalent to multiplying all elements in the i-th column by η. layer,l(i) This means synchronously reducing the weight of the outgoing edges propagated from source node i to all target nodes.

[0142] In the above calculations, when the system enters a severe divergent phase causing a sharp increase in deviation, the deduction term may exceed 1. At this point, the maximum value extraction function ignores the resulting negative values ​​and forcibly locks the target-level suppression factor at a preset lower bound. This preset lower bound can be 0.05. This operation ensures that all propagation weights, after undergoing severe reduction suppression, still maintain a physical baseline greater than 0, avoiding singular degeneration of the matrix and dynamic distortion.

[0143] Step 504: Traverse the node comprehensive risk vector, calculate the risk excess between the comprehensive risk value of each node and the preset reference risk benchmark; use the zero-value function to filter the risk excess, extract the effective risk excess greater than zero, and construct the target node enhancement factor in combination with the preset enhancement coefficient; use the target node enhancement factor to multiplicatively amplify the weights of all incoming edges of the corresponding node in the propagation operator.

[0144] In the second step of targeted reinforcement, the system aims to highlight the magnetic attraction effect of extremely vulnerable nodes in cascading failures. However, reinforcement operations cannot be blindly applied to all nodes, otherwise it will cause the entire propagation matrix to diverge again. The system employs a zero-value filtering mechanism with one-sided passage characteristics.

[0145] η node,i =1+μ*max(0,R i -R ref );

[0146] Where, η node,i The target node enhancement factor, μ, is the risk propagation enhancement coefficient, used to adjust the propagation intensity of the node during the risk propagation process. Its value is preset based on historical risk propagation characteristics or engineering experience and can be adaptively adjusted during the propagation process. max is the maximum value extraction function, 0 is the zero value, and R... i The node comprehensive risk value for the current assessment period is the i-th element in the node comprehensive risk vector R(t). ref This serves as a pre-set reference risk benchmark.

[0147] In the node-oriented enhancement step of the reconstruction operation, after obtaining the target node enhancement factor for all nodes, a node enhancement factor based on η is constructed. node,i D is the node reinforcement matrix with diagonal elements. node D node [i,i]=η node,i The propagation operator W, after undergoing hierarchical propagation suppression in the previous step, is... (l) Performing a left multiplication operation yields the propagation operator W after strengthening the incoming edges. (2) =D node *W (l) Since the propagation matrix in this application uses row notation to represent the target node, the left multiplication operation is equivalent to multiplying all elements in the row containing the target node i by η. node,i This enables the synchronous enhancement of the weights of all incoming edges to high-risk nodes.

[0148] In this mathematical construct, the system subtracts a preset reference risk benchmark from the risk value of each engineering node. The preset reference risk benchmark can be set to 0.50. If the node is in a relatively healthy state, the subtraction produces a negative risk excess, which the maximum value extraction function filters out to zero, ensuring that the enhancement factor of the target node strictly remains at the base value of 1, i.e., no enhancement operation is generated. Only when the node is in a highly dangerous state and produces a positive effective risk excess will this excess be proportionally amplified by a preset enhancement coefficient, thus converting it into an enhancement multiple greater than 1, achieving accurate targeted amplification of all incoming edge weights of the node.

[0149] In some optional implementations, if the recalculated network stability parameters still fail to return to the convergence range after reconstruction, a multi-round progressive reconstruction loop can be established. For example, when triggering the next round of reconstruction, the system can temporarily increase the preset suppression coefficient to 1.5 times the original value and execute the above three-step reconstruction instructions serially again until the maximum loop limit of three times is met. If convergence is still not achieved after multiple forced reconstructions, the highest-level network-wide uncontrollable alarm is issued, requiring direct manual intervention for shutdown and maintenance.

[0150] Example 6 details the mathematical mechanism for eliminating path intensity dimension differences through logarithmic normalization, the system comprehensive risk rating method based on multi-source index weighted fusion, and the offline objective function optimization and calibration process for core dynamic parameters.

[0151] Step 601: Extract the average steady-state risk value of the steady-state risk distribution; extract the dominant propagation path strength corresponding to the network propagation topology features during the evolution process, and use the preset reference path strength to perform logarithmic normalization on the dominant propagation path strength to obtain the normalized path strength.

[0152] After undergoing a complete cascaded dynamic evolution and reaching convergence, the steady-state risk values ​​of all engineering nodes in the network are extracted, and their arithmetic mean is calculated as the average steady-state risk value. This value macroscopically reflects the resting risk level of the entire network after undergoing multi-scale amplification and adaptive suppression. Simultaneously, a graph theory search algorithm is used to identify the propagation chain with the largest product of consecutive weights from the network propagation topology features, and this largest product is defined as the dominant propagation path strength. In actual engineering networks, as the number of hops in the propagation path increases, the path strength calculated directly may span multiple orders of magnitude, as the propagation weights of each segment may be greater than or less than 1. If this exponentially fluctuating index is directly linearly combined with other risk values ​​normalized to the [0,1] interval, it will lead to dimensional collapse, causing the fusion evaluation to lose its mathematical rationality.

[0153] To eliminate the inconsistency in dimensions and scale distortion caused by the path characteristics of product-type networks, the system introduces a logarithmic normalization operation to address extreme value fluctuations.

[0154] L norm =ln(1+L path ) / ln(1+L ref );

[0155] Among them, L norm Let L be the normalized path strength, ln be the natural logarithm function, and L be the path strength. path As the dominant propagation path strength, L ref The preset reference path strength should cover all possible maximum path strengths in the network.

[0156] Specifically, the preset reference path strength is calibrated based on the typical topological diameter and baseline edge weights of the engineering network, and is used to define the theoretically maximum expected propagation intensity. The system first adds 1 to the dominant propagation path strength and extracts its natural logarithm, then divides it by the logarithmized baseline value of the reference strength. The nonlinear compression mapping not only preserves the relative order of different path strengths but also smoothly constrains values ​​that might otherwise diverge to tens or even hundreds to a standard comparable interval between 0 and 1. To ensure that the normalized path strength falls within the [0,1] interval, the reference path strength L... ref It should be set to a value no less than the theoretical maximum single-step propagation weight in the network. In some alternative implementations, the calculated L can also be... norm Execute min(L) norm ,1) Truncation processing.

[0157] In some alternative implementations, if the system is running in a resource-constrained edge terminal environment, logarithmic normalization can be replaced with geometric mean normalization to avoid frequent calls to the high-overhead log-transcendental function calculation. Specifically, the dominant propagation path strength is square-rooted several times to directly offset the exponential dimensional expansion caused by the product operation, thus achieving dimensional uniformity.

[0158] Step 602: Construct a discrete phase indicator function to characterize whether the system is in a divergent phase state, and introduce a normalized spectral radius deviation index; based on a preset set of weight coefficients, weight and fuse the average steady-state risk value, normalized path strength, normalized spectral radius deviation index and discrete phase indicator function to generate a comprehensive risk assessment result for the system.

[0159] After obtaining the key features for eliminating the influence of dimensions, a normalized spectral radius deviation index and a penalty term mechanism are further introduced to highlight the threat posed by macroscopic instability. The discrete phase indicator function I... divThe output logic is as follows: when the dynamic stability determination system confirms that the network is in a divergent phase, I div =1; if the system is in a critical phase or a convergent phase, then I div =0. The normalized spectral radius deviation index is used to characterize the degree of deviation of the system stability from the critical boundary. The comprehensive risk assessment result of the system can be expressed as:

[0160] R sys =a*R avg +b*L norm +c*ρ norm +d*I div ;

[0161] Among them, R sys For the numerical scoring of the system's comprehensive risk assessment results, a, b, c, and d are the component weights in the preset set of weight coefficients, R. avg L is the average steady-state risk value. norm To normalize the path strength, ρ norm To normalize the spectral radius bias, I div This is a discrete phase indicator function.

[0162] The preset set of weighting coefficients can be set as a=0.4, b=0.2, c=0.2, d=0.2. Through linear weighted fusion, the system outputs a comprehensive score with a unified dimension and establishes a rigid mapping standard from continuous numerical values ​​to discrete security levels.

[0163] Specifically, the mapping standard for the system's comprehensive risk assessment results includes four defined risk levels. The first level is defined as a low-risk state, and the judgment condition is that the numerical score is strictly less than 0.25, and the discrete phase indicator function output is 0. At this time, the project is running smoothly and only routine periodic inspections are required.

[0164] The second level is a medium-risk state, which is determined by a numerical score between 0.25 and 0.50 and in a convergent phase, indicating that local hidden dangers are beginning to accumulate. The system will automatically increase the sampling frequency of monitoring data for high-risk nodes.

[0165] Level 3 is a high-risk state, determined by a numerical score between 0.50 and 0.75. At this level, the cascading propagation effect is significantly active, and a special investigation plan targeting the upstream nodes of the dominant propagation path must be activated.

[0166] Level 4 is an extremely high-risk state. The criteria for judgment are a numerical score greater than or equal to 0.75, or a discrete phase indicator function output of 1 and a score greater than 0.50. This state indicates that the system has an extremely high risk of cascading failure. Automatic flow limiting scheduling control logic must be triggered immediately, and severely polluted or deteriorated water supply branches must be physically cut off if necessary.

[0167] Step 603: Obtain the pre-stored historical typical risk evolution sample set; construct the parameter calibration objective function with the optimization objective of minimizing the trajectory error between the risk evolution prediction state and the historical typical risk evolution sample set.

[0168] The control parameters driving phase transitions, adaptive truncation, and physical attenuation in the aforementioned embodiments are not constants arbitrarily specified based on subjective experience. To ensure the engineering fitting accuracy of the evaluation system, an offline parameter pre-calibration procedure must be performed before the system is officially deployed online. Detailed monitoring records of major equipment failures, extreme weather impacts, or large-scale water quality anomalies that have occurred over the years are extracted from the operation management database and transformed into a historical typical risk evolution sample set with timestamp sequences.

[0169] J=∑((R model (t)-R obs (t)) 2 );

[0170] Where J is the sum of squared residuals output by the parameter calibration objective function, ∑ is the summation operator over all time sampling points, and R model (t) represents the risk evolution prediction state derived using the current parameter combination, R. obs (t) represents the actual state observations recorded in the historical typical risk evolution sample set.

[0171] Through the mathematical construction of summing the squared differences described above, the system establishes a nonlinear optimization objective solely aimed at minimizing the deviation between the model-produced trajectory and the historical actual development trajectory. Solving this objective function involves finding a set of hyperparameters that best fits the endogenous physical evolution laws of the target water diversion project.

[0172] Step 604: Solve the parameter calibration objective function using a parameter optimization algorithm to generate a pre-configured set of evolution control parameters; load the pre-configured set of evolution control parameters into the online operation process as the numerical calculation boundary conditions for performing structured modulation and reconstruction operations.

[0173] Parameter optimization algorithms such as grid search, gradient descent, or heuristic particle swarm optimization are employed to globally minimize the parameter calibration objective function in a high-dimensional space. During the optimization process, search boundaries and recommended ranges that conform to engineering principles need to be set for parameters with different physical meanings. Specifically, the spatial physical attenuation factor controlling the intensity of spatial attenuation is recommended to be optimized between 0.05 and 0.30; the upper bound of the coupling strength limiting the infinite amplification of positive feedback effects is recommended to be optimized between 1.0 and 3.0; the external disturbance modulation coefficient reflecting the impact of environmental degradation is recommended to be optimized between 0.2 and 0.5; and the hierarchical suppression coefficient, which plays a role in pressure reduction during reconstruction operations, is recommended to be searched between 0.1 and 2.0.

[0174] After multiple rounds of offline iterative convergence, the system extracts a set of parameters that minimizes the residual of the objective function and solidifies it into a pre-configured set of evolutionary control parameters. This parameter set is then distributed and loaded into the memory space of the online real-time monitoring server. The parameters, refined from historical real-world hazard data, will serve as the underlying numerical boundary conditions for each execution of multi-scale modulation mapping, nonlinear threshold triggering, phase identification, and reconstruction of truncation suppression by the online evaluation module. Through the decoupling and synergy between offline learning calibration and online rolling computation, this invention solves the technical problems of difficult parameter determination and system distortion in complex nonlinear dynamic models of large-scale water diversion projects.

[0175] Example 7: Specifically verify the above dynamic model and fully demonstrate the closed-loop dynamic risk assessment system for water diversion projects, from the division of engineering objects and nodes to the full business flow and algorithm implementation of comprehensive risk rating.

[0176] Step S1 involves identifying the engineering objects and dividing them into nodes. Taking a typical area of ​​a water diversion project as an example, this area includes a main line, a branch outlet, and two branch lines. The nodes at the main line level represent engineering units within the main line water conveyance channel whose risks can be independently assessed. The nodes at the branch outlet control level represent the branch outlet and its key control units. The nodes at the branch line level represent engineering units within the branch line water conveyance channel whose risks can be independently assessed. The final node set contains five nodes.

[0177] Step S2 involves classifying risk factors and determining data sources to establish a calculable risk factor system, categorizing node risk factors into four types: The first type is structural state risk factors, used to characterize the degree of anomalies in the structure itself or foundation. The second type is operational deviation risk factors, used to characterize the degree of deviation of nodes from the target allowable range under scheduling conditions. The third type is control reliability risk factors, used to characterize whether the support capabilities of control links and key equipment have declined. The fourth type is external disturbance factors, used to characterize the driving effects of the external environment.

[0178] Step S3 involves standardizing the indicators and calculating their anomalies, setting normal and severe thresholds for each indicator. A piecewise linear mapping is used to calculate the standardized anomalies.

[0179] s ij (t)=0,x ij (t)<=T1;

[0180] s ij (t)=(x ij (t)-T1) / (T2-T1),T1 <x ij (t) <T2;

[0181] s ij (t)=1,x ij (t)>=T2;

[0182] Among them, s ij (t) represents the standardized outlier of the j-th indicator at the i-th node, x ij (t) represents the observed value of the indicator, T1 is the normal threshold, and T2 is the severe threshold.

[0183] Step S4: Perform node comprehensive risk fusion, group the anomaly index into four categories: structure, operation, control, and external, and then perform multi-dimensional coupling fusion within each group according to weights to obtain four components.

[0184] R i (t)=α s *R s ,i+α o *R o,i +α c *R c,i +α e *R e,i ;

[0185] Among them, R i (t) represents the node's comprehensive risk value, t represents the current assessment time / period, and α s R represents the weights of the structural state group. s,i For the structural state risk component, α o To run the deviation group weights, R o,i To operate the deviation risk component, α c To control the weights of the reliability groups, R c,i To control the reliability risk component, α e For the weights of the external disturbance group, R e,i This represents the external disturbance risk component, also known as the external disturbance factor. The sum of the weights of all groups equals 1. The calculation results are used to determine the system risk status.

[0186] Step S5: Constructing the three-layer topology connection rules. This involves building a three-layer directed topology that reflects the coupling relationship between engineering entities and operational control. Connection rules are determined based on engineering entities and scheduling logic. Connections are established within the main line according to the water flow direction, from the main line to the branch line, and from the branch line to the tributary. A unified risk evolution equation is established:

[0187] R i (t+1)=f(R i (t),∑T ij R j (t),E(t),θ);

[0188] Among them, R i (t) represents the node's risk state, T ij Let θ be the propagation coefficient, E(t) be the external disturbance, and θ be the parameter set (γ, δ, α, μ). The determination result is used for subsequent risk warning and scheduling decisions.

[0189] Step S6: Construction of basic propagation weights. Based on the unified risk evolution equation, propagation weights are assigned to each directed edge to construct the basic propagation matrix.

[0190] w ij (t)=S ij *O ij (t)*I j *C ij (t);

[0191] Among them, w ij (t) represents the risk propagation intensity from source node i to target node j, S ij For structural coupling strength, O ij (t) represents the degree of operational coupling, I j C represents the importance of the target node. ij (t) represents the data credibility.

[0192] Step S7, multi-scale coupled propagation modulation, calculated based on the unified risk evolution equation, defines the aggregation operator Φ, whose element in the l-th row and j-th column is Φ. lj If node j belongs to set V l The value is then 1 / n l Otherwise, the value is 0, where n l Let be the number of nodes in level l. Define a feedback operator Ψ, whose element in the i-th row and l-th column is Ψ. il If node i belongs to set V l If the value is 1, then the value is 1; otherwise, the value is 0. Construct a multi-scale coupled modulation matrix.

[0193] M = I' + γ * Ψ * Φ; where M is the multi-scale modulation matrix, I' is the identity matrix, γ is the scale coupling strength parameter, Ψ is the feedback operator, and Φ is the aggregation operator.

[0194] The modulated propagation matrix is ​​the product of the multi-scale modulation matrix and the basic propagation matrix. Physically, it represents the layered coupling contribution, which is the sum of the average propagation weights of nodes at the same level, added to the original propagation weights. The coupling strength parameter is adaptively updated according to the following rules.

[0195] γ(t+1)=clip(γ(t)+ε*(R avg (t)-R ref ),0,γ max );

[0196] Where γ(t+1) is the coupling strength parameter for the next cycle, clip is the interval cutoff function, γ(t) is the coupling strength parameter for the current cycle, ε is the learning rate, and Rt+1 is the learning rate. avg (t) represents the average risk value of the entire network, which is the arithmetic mean of the comprehensive risk vector of all nodes in the network during the current period. R ref For reference risk level, γ max This represents the upper bound of the coupling strength.

[0197] Based on several known typical risk transmission scenarios in historical operational data, a calibration objective function is constructed.

[0198] J(γ,ε)=∑(||R model (t)-R observed (t)|| 2 );

[0199] Where J is the calibration objective function, ∑ is the summation operator, and R... model (t) represents the predicted risk state, R observed (t) represents the actual risk observation value.

[0200] Based on the spectral radius of the actual evolutionary propagation operator, the propagation state of the system is divided into convergent phase, critical phase, and divergent phase, and the phase transition condition is defined accordingly.

[0201] Step S8: Threshold Enhancement and External Perturbation Modulation. A dynamic trigger threshold is determined based on system-level external perturbation indicators. For nodes exceeding the dynamic trigger threshold, a tiered enhancement coefficient is determined, and the weights of all outgoing edges of the corresponding source nodes are enhanced to generate the comprehensive propagation operator W. nl .in:

[0202] R crit (t)=max(R crit_min ,R crit_0 -δ*R e_sys (t));

[0203] Among them, R crit (t) is the dynamic trigger threshold, max is the maximum value extraction function, and R crit_min R is the lower bound of the threshold. crit_0 The reference threshold is δ, the external disturbance modulation coefficient is R. e_sys (t) represents the system-level external disturbance index.

[0204] The system-level external disturbance index is defined as the risk-weighted average of the external disturbance factors of each node.

[0205] R e_sys (t)=∑(R i (t)*R e,i (t)) / ∑(R i (t));

[0206] Among them, R e_sys (t) represents the system-level external disturbance index, ∑ represents the summation operation, and R i (t) represents the node risk value, R e,i (t) represents the external perturbation factor of the node.

[0207] For nodes that meet the triggering conditions, increase the weight of all their outgoing edges.

[0208] w ij '=β i *w ij Among them, w ij 'This represents the enhanced outgoing edge weight, β' i For the enhancement coefficient, w ij This represents the original outgoing edge weight.

[0209] Step S9: Iteratively solve for risk propagation using the integrated propagation operator W generated in step S8. nl Based on this, an actual evolutionary propagation operator is constructed by combining the space physics attenuation factor, and the current comprehensive risk vector of the current assessment period is used as the basic risk. The steady-state risk vector containing multi-level propagation effects is solved by fixed-point iteration.

[0210] W prop =(1-μ d )*W nl ;

[0211] R (k+1) =clip(R(t)+W prop *R (k) ,0,1);

[0212] Among them, W prop For the actual evolutionary propagation operator, μ d R is the successive decay rate, also known as the spatial physical decay factor.(k+1) Let R(t) be the risk vector for the (k+1)th iteration, clip be the cutoff function, and R(t) be the comprehensive risk vector for the current evaluation period. (k) Let be the risk vector for the k-th iteration.

[0213] Under the linear condition of ignoring truncation, when the spectral radius of the actual evolution propagation operator is less than 1, the iterative steady-state solution is as follows.

[0214] R stable =(I'-W prop ) (-1) *R(t);

[0215] Among them, R stable Let I' be the steady-state risk vector, and W be the identity matrix. prop For actual evolution propagation operators.

[0216] Step S10: Perform phase determination driven by spectral radius. Calculate the spectral radius of the propagation operator.

[0217] ρ actual =(1-μ d )*ρ(W nl );

[0218] Where, ρ actual μ is the spectral radius of the actual evolutionary propagation operator. d The successive decay rate, i.e., the space physical decay factor, ρ(W) nl ) represents the spectral radius of the integrated propagation operator. The spectral radius is used to characterize the stability state of risk propagation in a water diversion project system.

[0219] The three-phase state is defined by the relationship between the spectral radius and the critical value 1. The first is the convergent phase, i.e., the stable state, determined by the spectral radius being strictly less than 1-ε. ρ , ε ρ The first is the tolerance parameter. The second is the critical phase state, determined by the spectral radius being between 1 ± ε. ρ The third is the divergent phase, i.e., the unstable state, determined by the spectral radius being strictly greater than 1 + ε. ρ .

[0220] Step S11: Perform dynamic reconstruction of the propagation operator. Reconstruction is triggered if any one of the following conditions is met: Trigger condition one: the system enters a divergent phase. Trigger condition two: node risk exceeds a warning value. Trigger condition three: system-level external disturbance exceeds a critical threshold.

[0221] The first step is hierarchical propagation suppression, which involves calculating the suppression factor at each level.

[0222] ρ dev =max(0,ρ actual -1);

[0223] η layer,l =max(η min ,1-α l *ρ dev );

[0224] Where, η layer,l η is the hierarchical suppression factor, max is the maximum value extraction function, and η is the maximum value extraction function. min As the lower bound of the inhibitory factor, α l ρ is the hierarchical suppression coefficient. actual Let ρ be the spectral radius of the actual evolution propagation operator. dev This represents the positive deviation of the actual evolution propagation operator spectrum radius from the stability critical value of 1, i.e., the deviation magnitude of the network dynamics stability characteristic parameter.

[0225] After determining the target level suppression factor for each level, a level reduction matrix D is constructed with the level suppression factor of each node as its diagonal element. layer D layer [i,i]=η layer,l(i) Let l(i) represent the level to which node i belongs. Perform a right multiplication operation W on the synthesis propagation operator. (l) =W nl *D layer This reduces the weights of all outgoing edges from each source node proportionally according to the suppression factor of its respective level. Since the propagation matrix in this application uses column notation for source nodes, the right multiplication operation is equivalent to multiplying all elements in the i-th column by η. layer,l(i) This means synchronously reducing the weight of the outgoing edges propagated from source node i to all target nodes.

[0226] The second step is to target and enhance node risk, with the following enhancement factors:

[0227] η node,i =1+μ*max(0,R i -R ref );

[0228] Where, η node,i R is the target node enhancement factor, μ is the enhancement coefficient, max is the maximum value extraction function, and R is the maximum value extraction function. i R represents the node risk value for the current assessment period. ref For reference risk level.

[0229] The target node enhancement factor is used to perform weight enhancement on the weights of all incoming edges of the node.

[0230] In the node-oriented enhancement step of the reconstruction operation, after obtaining the target node enhancement factor for all nodes, a node enhancement factor based on η is constructed. node,i D is the node reinforcement matrix with diagonal elements. node D node[i,i]=η node,i The propagation operator W, after undergoing hierarchical propagation suppression in the previous step, is... (l) Performing a left multiplication operation yields the propagation operator W after strengthening the incoming edges. (2) =D node *W (l) Since the propagation matrix in this application uses row notation to represent the target node, the left multiplication operation is equivalent to multiplying all elements in the row containing the target node i by η. node,i This enables the synchronous enhancement of the weights of all incoming edges to high-risk nodes.

[0231] The third step is edge structure pruning, which sets the weight of edges that are lower than the threshold after reconstruction to 0.

[0232] w ij '''=w ij ''*I(w ij ''>=w min );

[0233] Among them, w ij ''' represents the weight after pruning, w ij '' represents the input weights, I represents the indicator function, and w min This is the trimming threshold.

[0234] Step S12: Unify the evolution equations during the evaluation cycle. The state transitions of the system between adjacent evaluation cycles are described by unified equations.

[0235] R(t+1)=clip((I'-W prop (t)) (-1) *[(1-λ e )*R(t)+λ e *R new [(t+1)],0,1);

[0236] Where R(t+1) is the state vector of the next cycle, clip is the cutoff function, I' is the identity matrix, and W prop (t) is the actual evolutionary propagation operator, λ e R is the fusion coefficient of old and new data, R(t) is the inherent risk of the current period, and R new (t+1) represents the new acquisition risk, which is the initial inherent risk vector for the next acquisition cycle.

[0237] Step S13: Dominant propagation path identification. Define the path propagation strength as the product of the weights of all edges on the path. Select the path with the highest propagation strength as the dominant propagation path. Perform logarithmic normalization on the path strength.

[0238] The path strength is initially logarithmically normalized to compress the numerical dynamic range:

[0239] Lnorm =ln(1+L path ) / ln(1+L ref );

[0240] Among them, L norm Let L be the normalized path strength, ln be the natural logarithm function, and L be the path strength. path As the dominant propagation path strength, L ref The preset reference path strength.

[0241] The reference path strength L ref Pre-calibrated based on the topological diameter and typical propagation weight statistics of the water diversion project.

[0242] Step S14: Conduct a comprehensive risk assessment. Construct a comprehensive risk measurement index.

[0243] We introduce a normalized spectral radius deviation index and a discrete phase state indicator function to more precisely characterize the contribution of system stability to the overall score.

[0244] The normalized spectral radius deviation index is: ρ norm =min(1,max(0,(ρ actual -1) / ε ρ ));

[0245] The discrete phase indicator function is defined as: when ρ actual >1+ε ρ At that time, I div =1; otherwise, I div =0.

[0246] The overall risk score is: R sys =a*R avg +b*L norm +c*ρ norm +d*I div ;

[0247] Among them, R sys For the comprehensive risk score, a, b, c, and d are weighting coefficients, and R0 avg L is the average steady-state risk value. norm To normalize the path strength, ρ norm For the normalized spectral radius deviation, ρ actual I is the spectral radius of the actual evolution propagation operator. div ε is the discrete phase indicator function. ρ This is the tolerance parameter.

[0248] The discrete phase indicator function is introduced as a penalty term to perform discontinuous amplification correction on the comprehensive risk score when the system is in a divergent phase state.

[0249] In another embodiment, the risk level determination rules are as follows: Level I, low risk, is determined by a comprehensive risk score less than 0.25 and in a convergent phase. Level II, medium risk, is determined by a comprehensive risk score between 0.25 and 0.50 and in a convergent or critical phase. Level III, high risk, is determined by a comprehensive risk score between 0.50 and 0.75, or in a critical phase with a score greater than or equal to 0.35. Level IV, extremely high risk, is determined by a comprehensive risk score greater than or equal to 0.75, or in a divergent phase with a score greater than or equal to 0.50.

[0250] Example 8: The above dynamic model is specifically verified. Through a simplified water conveyance engineering network containing five channel nodes, the entire numerical deduction process of multi-scale modulation, phase determination, threshold enhancement and adaptive reconstruction in the closed-loop dynamic risk assessment model is fully demonstrated.

[0251] Consider a water conveyance system consisting of five canal segment nodes. Node v1 describes the upper section of the main canal, and its hierarchy is the main canal. Node v2 describes the middle section of the main canal, and its hierarchy is the main canal. Node v3 describes the lower section of the main canal, and its hierarchy is the main canal. Node v4 describes branch canal A, and its hierarchy is branch canal. Node v5 describes branch canal B, and its hierarchy is branch canal. The directed edges, i.e., the directions of water flow and risk propagation, include v1 pointing to v2, v2 pointing to v3, v1 pointing to v4, v2 pointing to v5, and v4 pointing to v5. The main canal has 3 hierarchical nodes, and the branch canals have 2 hierarchical nodes.

[0252] Assume the overall risk vector and external disturbance factor for the current assessment period are as follows: Node v1 has an overall risk value of 0.45 and an external disturbance factor of 0.20. Node v2 has an overall risk value of 0.35 and an external disturbance factor of 0.15. Node v3 has an overall risk value of 0.20 and an external disturbance factor of 0.10. Node v4 has an overall risk value of 0.30 and an external disturbance factor of 0.25. Node v5 has an overall risk value of 0.25 and an external disturbance factor of 0.10.

[0253] The non-zero elements of the basic propagation matrix are as follows: The basic propagation weight of edge v1 pointing to v2 is 0.40, meaning that upstream structural deterioration propagates to the midstream. The basic propagation weight of edge v2 pointing to v3 is 0.50, meaning that midstream risk propagates downstream. The basic propagation weight of edge v1 pointing to v4 is 0.30, meaning that the risk propagates from the main canal to branch canal A. The basic propagation weight of edge v2 pointing to v5 is 0.20, meaning that the risk propagates from the middle section of the main canal to branch canal B. The basic propagation weight of edge v4 pointing to v5 is 0.40, meaning that the risk propagates from branch canal A to branch canal B.

[0254] Taking the scale coupling strength γ=0.5, the upper limit of the strength γ max =2.0, learning rate ε=0.1, reference risk level Rref =0.30. After the aggregation operator Φ and the feedback operator Ψ are constructed according to their definitions, the modulation matrix is ​​as follows:

[0255] M = I' + 0.5 * Ψ * Φ; where M is the multi-scale modulation matrix, I' is the identity matrix, Ψ is the feedback operator, and Φ is the aggregation operator.

[0256] The specific values ​​of matrix M are a block matrix, and the elements of the main canal sub-blocks are:

[0257] The sub-block elements are (7 / 6, 1 / 6, 1 / 6; 1 / 6, 7 / 6, 1 / 6; 1 / 6, 1 / 6, 7 / 6), the branch sub-block elements are (5 / 4, 1 / 4; 1 / 4, 5 / 4), and the remaining cross-layer elements are 0. The calculated and corrected multi-scale coupled modulation propagation matrix is ​​as follows: W Θ =M*W0; where W Θ Let M be the propagation matrix after multi-scale coupling modulation, M be the multi-scale modulation matrix, and W0 be the basic propagation matrix.

[0258] In normal operating scenario A, since there are no nodes exceeding the dynamic trigger threshold, the enhancement coefficient for each node is 1.0. Therefore, the comprehensive propagation operator W... nl Degenerates into the coupling propagation matrix W Θ Matrix W Θ The non-zero column vector elements are the first column (0.067, 0.467, 0.067, 0.375, 0.075), the second column (0.083, 0.083, 0.583, 0.050, 0.250), and the fourth column (0, 0, 0, 0.100, 0.500).

[0259] In scenario A under normal operating conditions, the parameter is taken as the spatial physical attenuation factor μ. d =0.15. W prop =(1-0.15)*W Θ =0.85*W Θ Due to the strongly connected component structure of the propagation network, matrix W Θ The spectral radius is determined by the sub-block formed by nodes v1 and v2. The trace of the sub-block's characteristic matrix is ​​0.150, and its determinant is 0.067 × 0.083 - 0.083 × 0.467 = -0.0333. λ1 ​​= (0.150 + sqrt(0.150) / (2π)) 2 +4*0.0333)) / 2=0.272; the eigenvalue of the v4 sub-block is 0.100, and the eigenvalues ​​of the other sub-blocks are 0. Therefore, the spectral radius ρ=0.272. The spectral radius ρ of the actual evolutionary propagation operator. actual =0.85*0.272=0.231.

[0260] Since 0.231 < 0.95, the system is determined to be in a convergent phase, i.e., a stable state. Cascade propagation iterative evolution is performed, and the initial risk state vector is R(0) = (0.450, 0.350, 0.200, 0.300, 0.250).

[0261] The vector for the first iteration is (0.500, 0.553, 0.399, 0.484, 0.481);

[0262] The vector for the second iteration is (0.518, 0.588, 0.503, 0.524, 0.605);

[0263] The vector for the third iteration is (0.521, 0.597, 0.521, 0.534, 0.631).

[0264] Continue iterating until the difference in the infinity norm of two adjacent risk vectors is less than the preset convergence tolerance (e.g., one ten-thousandth), and finally converge to obtain the steady-state risk distribution vector R. stable =(0.522,0.600,0.527,0.538,0.639). It has been verified that this steady-state value is consistent with the analytical solution (I'-W). prop ) (-1) ×R(t) is consistent. The average steady-state risk value for the entire network is 0.565. The risk of each node is higher than the initial value, reflecting the amplification effect of cascading propagation. Among them, node v5 has the largest risk increase because it receives dual propagation from both v2 and v4. At this time, there is no condition to trigger reconstruction, and it directly enters the comprehensive rating stage.

[0265] In scenario B, under abnormal operating conditions, it is assumed that the system encounters extreme operating conditions in another evaluation period, leading to an increase in overall risk. The overall risk vector under abnormal operating conditions is R = (0.80, 0.70, 0.40, 0.55, 0.35). The external disturbance vector under abnormal operating conditions is R... e =(0.60,0.45,0.20,0.55,0.30).

[0266] Calculate system-level external disturbance indices:

[0267] R e_sys =(0.80*0.60+0.70*0.45+0.40*0.20+0.55*0.55+0.35*0.30) / (0.80+0.70+0.40+0.55+0.35)=0.458.

[0268] Take the baseline threshold R crit_0 =0.55, external disturbance modulation coefficient δ=0.5, lower threshold R crit_min =0.10. Calculate the dynamic trigger threshold: R crit=max(0.10,0.55-0.5*0.458)=0.321.

[0269] The trigger conditions for each node are as follows:

[0270] v1: Ri=0.80, ≥0.321 trigger, graded enhancement coefficient β1=2.5, 0.75≤0.80<0.90;

[0271] v2: Ri=0.70, ≥0.321 trigger, graded enhancement coefficient β2=2.0, 0.60≤0.70<0.75;

[0272] v3: Ri=0.40, ≥0.321 trigger, graded enhancement coefficient β3=1.5, 0.321≤0.40<0.60;

[0273] v4: Ri=0.55, ≥0.321 trigger, graded enhancement coefficient β4=1.5, 0.321≤0.55<0.60;

[0274] v5: Ri=0.35, ≥0.321 trigger, graded enhancement coefficient β5=1.5, 0.321≤0.35<0.60.

[0275] Enhanced post-propagation matrix W nl The weights of each outgoing edge are multiplied by the corresponding enhancement coefficient of the source node, effectively performing a right multiplication of the matrix to amplify the outgoing edges. The outgoing edge weight of node v1 is multiplied by 2.5, the outgoing edge weight of node v2 by 2.0, and the outgoing edge weight of node v4 by 1.5. The enhanced matrix W is then calculated. nl The first column of elements becomes (0.168, 1.168, 0.168, 0.938, 0.188), the second column of elements becomes (0.166, 0.166, 1.166, 0.100, 0.500), and the fourth column of elements becomes (0, 0, 0, 0.150, 0.750).

[0276] The spectral radius is calculated as follows: sub-block trace = 0.334, determinant det = 0.168 × 0.166 - 0.166 × 1.168 = -0.166. λ1 = (0.334 + sqrt(0.334)) 2 +4*0.166)) / 2=0.608. Spectral radius ρ=0.608. Actual evolution propagation operator spectral radius ρ_actual=0.85×0.608=0.517. 0.517<0.95, the system is still in a convergent phase and no reconstruction is needed.

[0277] To demonstrate the reconfiguration process, it is assumed that the comprehensive risk vector R further increases under extreme scenarios, and the system-level external disturbance index rises to 0.677. crit=max(0.10,0.55-0.5*0.677)=0.211. All nodes trigger enhancements, which carries an extremely high risk of causing the matrix spectral radius to spike after enhancement; assuming the calculated spectral radius increases to 1.35. ρ actual =0.85 * 1.35 = 1.148. Since 1.148 > 1.05, the system enters a divergent phase.

[0278] Perform adaptive triggering reconstruction operation. Take the hierarchical suppression coefficient α. l The lower bound of the inhibition factor is η, which is 2.0. min η is 0.05. layer =max(0.05,1-2.0*(1.148-1))=0.704. The edge weights at each level are multiplied by 0.704 to complete the hierarchical propagation suppression processing. Next, node risk-oriented reinforcement processing is performed. Taking node v1 as an example:

[0279] η node,1 =1 + 0.5 * max(0, 0.92 - 0.50) = 1.21. The weight of the incoming edge of node v1 is multiplied by 1.21. Then, edge pruning is performed, deleting redundant edges with weights less than 0.01. The spectral radius is recalculated after reconstruction. Because the hierarchical propagation suppression process significantly and uniformly reduces the weights across the entire network, subsequent node-directed reinforcement only locally amplifies the incoming edges of a few high-risk nodes. Furthermore, edge pruning further removes weakly propagating edges. Therefore, the actual spectral radius after reconstruction is approximately ρ. actual_re ≈0.704×1.148≈0.808. Since 0.808<0.95, the system is forced to return to the convergent phase, and the anti-divergence reconstruction mechanism is effective.

[0280] The dominant path and comprehensive rating process are as follows, returning to the normal operating condition of scenario A. By traversing all directed edges of the coupling propagation matrix and their multi-order combinations, the propagation chain with the largest product of consecutive weights is identified as the dominant propagation path. In this example, the dominant propagation path is determined to be v2 pointing to v3, with a corresponding propagation strength of 0.583. The reference path strength L is taken. ref =1.00, normalized using the modified translation logarithm formula: L norm =ln(1+0.583) / ln(1+1.00)=0.663.

[0281] The comprehensive rating is calculated as follows: the average steady-state risk value is 0.565, the normalized path strength is 0.663, the divergence deviation is 0, and the discrete phase indicator function output is 0.

[0282] R sys =0.40*0.565+0.20*0.663+0.20*0+0.20*0=0.359.

[0283] The score is 0.359 and is in a convergent phase, ultimately classified as medium risk. Recommended measures include increasing the inspection frequency of the upper and middle sections of the main canal involved in the dominant propagation path. In the extreme scenario of reconfiguration, the score will be significantly increased due to the triggering of the discrete phase penalty function, ultimately resulting in an automatic classification as high risk or extremely high risk.

[0284] Example 9 provides another implementation of a risk cascading propagation and risk assessment method for water transfer projects based on multi-level topology, comprising the following steps:

[0285] A multi-level topology network model was constructed, dividing the water diversion project into main line layer nodes, control layer nodes, and branch line layer nodes, and cross-level connection relationships between nodes were established.

[0286] A basic risk propagation matrix is ​​constructed and structured modulation is performed. Based on the comprehensive risk vector of each node, a nonlinear enhancement mapping is performed on the basic risk propagation matrix to obtain a comprehensive propagation operator, which is used to characterize the propagation intensity and direction of risk in a multi-level topological network.

[0287] A risk cascade propagation dynamic model is established, an actual evolution propagation operator is constructed based on the comprehensive propagation operator, and the node risk state is iteratively evolved based on the actual evolution propagation operator to obtain the system risk propagation process and steady-state risk distribution.

[0288] A propagation stability determination mechanism based on spectral radius is constructed. By calculating the spectral radius of the actual evolutionary propagation operator, the stability state of risk propagation in the water transfer project system is characterized, and the system is divided into convergent phase, critical phase, or divergent phase based on this. In the equivalent implementation, the spectral radius of the comprehensive propagation operator can also be calculated first, and then the spectral radius of the actual evolutionary propagation operator can be obtained by combining the space physics attenuation factor.

[0289] An adaptive reconstruction mechanism for the propagation operator driven by the spectral radius is established. When the system is determined to be in a divergent phase or exceeds a preset stability threshold, structural reconstruction and weight suppression operations are performed on the integrated propagation operator to reduce the risk propagation intensity and restore system stability.

[0290] A closed-loop risk evolution mechanism of propagation-determination-reconstruction-repropagation is formed. By constructing a reconstruction actual evolution propagation operator from the reconstruction comprehensive propagation operator, and performing iterative calculations based on the reconstruction actual evolution propagation operator until the system risk propagation meets the convergence condition and a stable risk distribution is obtained.

[0291] Based on the characteristics of stable risk distribution and risk propagation paths, the comprehensive risk assessment results of the water diversion project system are output.

[0292] Specifically, the structure of the integrated propagation operator is adaptively updated according to the determination result of the network dynamic stability characteristic parameter, forming a closed-loop evolution mechanism of propagation-determination-reconstruction-repropagation.

[0293] In the multi-level topology network model, nodes are divided into trunk water conveyance nodes, control hub nodes and branch water conveyance nodes according to the engineering structure. Cross-level connection edges are established through physical connection relationships and scheduling control relationships to form a directional multi-level coupled topology structure.

[0294] The node comprehensive risk vector is composed of multiple risk factors, including structural state risk factors, operational deviation risk factors, control reliability risk factors, and external disturbance factors, and a risk characterization value with unified dimensions is obtained through standardization.

[0295] The integrated propagation operator is obtained by performing a nonlinear enhancement mapping on the basic risk propagation matrix. The nonlinear enhancement mapping adaptively modulates the propagation weights according to the node risk status, thereby strengthening the propagation influence of high-risk nodes and suppressing the propagation of low-risk nodes.

[0296] The risk cascade propagation dynamics model is implemented through iterative calculation. The risk state of each node is updated according to the propagation operator in each iteration cycle, and the risk value is restricted to a preset range by a truncation function to ensure numerical stability.

[0297] In the propagation stability determination mechanism, the spectral radius of the actual evolutionary propagation operator is calculated and compared with a preset stability threshold to determine the risk propagation state of the system. The spectral radius is used to characterize the amplification or attenuation characteristics of the risk propagation process. In the equivalent implementation, the spectral radius of the comprehensive propagation operator can also be calculated first, and then the spectral radius of the actual evolutionary propagation operator can be obtained by combining the space physics attenuation factor.

[0298] Based on the deviation between the spectral radius and the unit value, a spectral radius deviation index is constructed, and the system risk propagation state is divided into convergent phase, critical phase and divergent phase according to the spectral radius deviation index.

[0299] The adaptive reconstruction mechanism of the propagation operator includes:

[0300] Truncation, reduction, or structural adjustment operations are performed on the propagation weights to reduce the spectral radius of the propagation operator, thereby transforming the system from a divergent phase to a convergent phase.

[0301] Based on the propagation operator, the risk-dominant propagation path is identified. The propagation intensity of the path is calculated and normalized. Combined with the steady-state risk value of the node, a comprehensive risk index of the system is constructed.

[0302] Preferably, a system for risk cascading propagation and system risk assessment of water diversion projects based on a multi-level topology is provided, comprising: a topology construction module for constructing a multi-level topology; a risk propagation modeling module for establishing risk propagation relationships and nonlinear mapping mechanisms; a hierarchical coupling analysis module for realizing inter-layer coupling modeling; and a risk assessment module for calculating risk propagation characteristic parameters and determining risks.

[0303] By constructing a multi-level topological network model of the water diversion project, different engineering structures such as main lines, branch lines, and tributaries are uniformly abstracted, and directed propagation relationships between nodes are established to realize a structured expression of the risk transmission path of complex water diversion systems. On this basis, a hierarchical mapping modulation mechanism and a nonlinear enhancement mechanism are introduced to construct a comprehensive propagation operator, realizing bidirectional modulation of the risk interaction relationship between different levels and adaptive amplification of the risk propagation capability of key nodes.

[0304] Furthermore, this invention constructs a risk propagation phase determination method based on the spectral radius of the propagation operator. By comparing the spectral radius with the stability threshold, the risk propagation state of the system is divided into stable phase, critical phase, and divergent phase, thereby achieving quantitative determination of the overall stability of the system.

[0305] When the system is in a divergent phase, a dynamic reconstruction mechanism of the propagation operator is introduced. Through structural control methods such as hierarchical suppression, node strengthening, and edge weight pruning, the original propagation network is adaptively adjusted to suppress the risk cascading amplification effect and realize the controllability of the system risk propagation process.

[0306] Based on this, the system risk is iteratively evolved and calculated using the reconstructed propagation operator to obtain the dynamic change process of the system risk. By combining the node risk status, key risk transmission paths and high-risk nodes are identified, thus realizing a comprehensive assessment of the system risk of the water diversion project.

[0307] The core of this invention lies in constructing a closed-loop dynamic mechanism of propagation-determination-reconstruction-repropagation. In this mechanism, the structure of the propagation operator adaptively evolves with the system's stability state. By applying the network dynamics stability determination result inversely to the structural adjustment of the propagation operator, the continuity constraint of the risk propagation process in the spatiotemporal dimension and its self-consistency in a mechanical sense are achieved. This closed-loop mechanism differs from traditional static propagation or unidirectional cascade models. It introduces a phase determination and structural reconstruction linkage mechanism based on spectral radius, enabling the propagation operator to have adaptive control capabilities during dynamic evolution, thereby achieving stability control and nonlinear modulation of system-level risk propagation. By using the spectral radius of the propagation operator as a system stability criterion and feeding it back into the dynamic reconstruction of the propagation structure, the closed-loop mechanism transforms the risk propagation process from passive diffusion to controllable evolution.

[0308] This invention constructs an adaptive reconstruction closed-loop mechanism based on spectral radius-driven propagation operators. Under a multi-level topology, a comprehensive propagation operator is constructed through nonlinear enhancement mapping, and the spectral radius of the propagation operator is calculated in real time during the risk propagation process to characterize the stability state of the system's risk propagation. When the system enters a divergent phase or approaches an unstable critical state, the structural reconstruction and weight suppression of the propagation operator are automatically triggered to regulate the risk propagation intensity. The system state is then regressed to a convergent phase through re-propagation calculation, ultimately forming a closed-loop risk evolution control mechanism.

[0309] By introducing multi-level topology modeling and nonlinear propagation mechanisms, the accuracy of risk transmission path identification in water transfer projects was improved; the spectral radius phase state determination method enabled quantitative analysis of system stability; the dynamic reconstruction mechanism of propagation operators effectively suppressed risk cascading diffusion and improved the system's risk control capabilities; and the scientific rigor and reliability of risk assessment and early warning during the operation of water transfer projects were enhanced.

[0310] This application introduces a multi-scale coupling operator that maps nodes to levels bidirectionally and constructs a dynamic evolution threshold model driven by system-level external disturbances. This approach breaks the limitations of fixed propagation weights, allowing the overall macroscopic situation to modulate the propagation intensity of local single points, and the system trigger threshold can be dynamically reduced as the extreme external environment deteriorates, thus reproducing the physical process of nonlinear amplification of engineering vulnerability with worsening conditions. It solves the problems of static models being unable to characterize cross-level nonlinear transitions and lacking macroscopic feedback.

[0311] This application forcibly incorporates a spatial physical attenuation factor into the cascaded propagation operator, ensuring that the network iterative evolution satisfies the Neumann series convergence condition from an algebraic topological perspective. Simultaneously, it extracts the operator spectral radius as a network dynamic characteristic parameter, defining the absolute boundaries of risk propagation between the convergent, critical, and divergent phase states. This solves the shortcomings of traditional linear iteration, which is prone to numerical divergence and has ambiguous phase transition boundaries.

[0312] This application constructs an adaptive reconfiguration closed-loop control mechanism to prevent physical distortion. When the system determines that it has entered a divergent phase, it actively triggers a three-step serial reconfiguration operation, including lower bound positive value truncation protection, hierarchical suppression, directional reinforcement, and structural pruning. This avoids the physical fallacy caused by negative weights and integrates the rigid reshaping process of network propagation structure through disaster prevention scheduling intervention into the dynamic closed loop. It solves the problem that static evaluation lacks an active intervention mechanism and is prone to backpropagation fallacy.

[0313] The preferred embodiments of the present invention have been described in detail above. The various specific technical features described in the above embodiments can be combined in any suitable manner without contradiction. To avoid unnecessary repetition, the present invention will not further describe the various possible combinations.

Claims

1. A method for risk cascade propagation and risk assessment of water diversion project based on multi-level topology structure, characterized in that, include: Obtain the topology network of the water transfer project based on the structure of the main line, the water outlet and the branch line, and generate the node comprehensive risk vector of each node based on the multi-source project operation data; A basic risk propagation matrix is ​​constructed based on the physical connections in the topology network of the water diversion project, and a comprehensive propagation operator is generated by structurally modulating the basic risk propagation matrix based on the node comprehensive risk vector. The node comprehensive risk vector is cascaded and iteratively evolved based on the comprehensive propagation operator. During the evolution process, the network dynamic stability characteristic parameters of the comprehensive propagation operator are continuously calculated to determine the system phase. When the system is determined to be in a divergent phase state based on the network dynamics stability characteristic parameters, an adaptive triggering reconstruction operation is performed on the integrated propagation operator to reduce the propagation intensity of the integrated propagation operator, generating a reconstructed integrated propagation operator. Based on the reconstructed integrated propagation operator, cascade propagation iterative evolution is continued until convergence, obtaining the steady-state risk distribution and the network propagation topology characteristics during the evolution process. An adaptive triggering reconstruction operation is performed on the synthesized propagation operator to reduce the propagation strength of the synthesized propagation operator, generating a reconstructed synthesized propagation operator, including: Perform hierarchical propagation suppression processing on the integrated propagation operator to reduce the propagation weights corresponding to high-risk levels; Based on the node comprehensive risk vector, node risk-oriented reinforcement processing is performed on the propagation operator after hierarchical propagation suppression processing to enhance the weight of incoming edges corresponding to high-risk nodes. Using a preset pruning threshold, edge structure pruning is performed on the propagation operator after it has undergone node risk-oriented reinforcement processing. Propagation weights that are less than the pruning threshold are reset to zero, and a reconstructed comprehensive propagation operator is generated. Based on the steady-state risk distribution and combined with the network propagation topology characteristics, the system's comprehensive risk assessment results are output.

2. The method according to claim 1, characterized in that, The basic risk propagation matrix is ​​structurally modulated based on the node-integrated risk vector to generate an integrated propagation operator, including: The basic risk propagation matrix is ​​coupled and modulated at multiple scales using a pre-constructed node-hierarchy bidirectional mapping relationship to obtain the coupled propagation matrix; The coupled propagation matrix is ​​subjected to nonlinear enhancement modulation based on the node-integrated risk vector to generate the integrated propagation operator.

3. The method according to claim 2, characterized in that, By utilizing a pre-constructed node-hierarchy bidirectional mapping relationship, the basic risk propagation matrix is ​​subjected to multi-scale coupling modulation to obtain the coupled propagation matrix, which includes: Based on pre-built aggregation operators for characterizing the mapping from nodes to levels and feedback operators for characterizing the mapping from levels to nodes, combined with pre-configured scale coupling strength parameters, a multi-scale modulation matrix is ​​constructed. The coupling propagation matrix is ​​obtained by multiplying the multi-scale modulation matrix with the basic risk propagation matrix.

4. The method according to claim 2, characterized in that, Based on the node-integrated risk vector, nonlinear enhancement modulation is performed on the coupled propagation matrix to generate an integrated propagation operator, including: The system-level external disturbance index is obtained by weighting the external disturbance factors of each node and the node comprehensive risk vector obtained in real time. The preset baseline threshold is down-modulated using system-level external disturbance indicators to determine the dynamic trigger threshold; Extract the nodes that exceed the limit from the node comprehensive risk vector and the dynamic trigger threshold, and determine the graded enhancement coefficient based on the risk amplitude of the nodes that exceed the limit; The weights of outgoing edges corresponding to the overlimit nodes in the coupling propagation matrix are amplified by using hierarchical enhancement coefficients to generate a comprehensive propagation operator.

5. The method according to claim 1, characterized in that, The node comprehensive risk vector is cascaded and iteratively evolved based on the comprehensive propagation operator, including: Obtain a preset spatial physics attenuation factor, scale the integrated propagation operator based on the spatial physics attenuation factor, and construct the actual evolution propagation operator; Using the node comprehensive risk vector as the initial iteration state, the fixed-point iteration with bounded truncation is performed using the actual evolution propagation operator.

6. The method according to claim 1, characterized in that, The network dynamic stability characteristic parameter is the spectral radius; The network dynamic stability characteristic parameters of the integrated propagation operator are continuously calculated, including: The spectral radius is obtained by extracting the maximum eigenvalue modulus of the synthesized propagation operator.

7. The method according to claim 6, characterized in that, Determining whether a system is in a divergent phase based on network dynamics stability characteristic parameters includes: The spectral radius is compared with the preset stability critical value and the preset tolerance parameter. When the spectral radius is greater than the sum of the stability critical value and the tolerance parameter, the system is determined to be in a divergent phase.

8. The method according to claim 1, characterized in that, In addition to being triggered when the system is determined to be in a divergent phase, the adaptive triggering reconfiguration operation is also triggered when at least one of the following conditions is met: Extract the maximum node risk amplitude from the node comprehensive risk vector, and trigger when the maximum node risk amplitude is greater than the preset node risk warning threshold; Based on real-time acquired system-level external disturbance indicators, the system is triggered when the system-level external disturbance indicators exceed the preset external disturbance critical threshold.

9. A risk cascading propagation and risk assessment system for water diversion projects based on a multi-level topology, characterized in that, include: Memory, used to store computer programs; A processor for executing a computer program to implement the steps of the method as described in any one of claims 1 to 8.

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