Dynamic Identification Method for the Risk Evolution Law of Complex Water Network Systems

Abstract

The present invention provides a method for dynamically identifying the risk evolution law of a complex water network system, and the steps are as follows: collect basic information and identify risk factors to obtain a risk factor sample set; divide the water conservancy projects in the water network research area into a three-level mutually feeding hierarchical structure to construct a multi-objective real-time risk scheduling model, and solve to obtain a risk scheduling solution set; combine the risk scheduling solution set and establish real-time scheduling risk propagation models for each level and a global real-time risk propagation network model for the hierarchical structure of the complex water network system; based on the global real-time risk propagation network model, identify the vulnerable nodes and key risk paths of each layer respectively, and perform cross-level node domination mapping on them to identify the vulnerable levels and key risk paths of the entire water network system. The present invention comprehensively considers multiple uncertainties, improves the calculation efficiency and the accuracy of risk positioning, and has important significance for the risk control of the water network system.

Description

Technical Field

[0001] The present invention relates to the technology of water network system risk assessment, and particularly to a method for dynamically identifying the risk evolution law of complex water network systems. Background Art

[0002] Existing methods for analyzing the risk evolution law of water network systems include: Markov chain, which describes the evolution process of a certain stochastic process in different states by establishing a Markov transition matrix. The stochastic process has the characteristic of no aftereffect, and there are limitations in application when dealing with problems with aftereffect; Fault Tree Method, which decomposes the factors constituting an accident into individual events step by step, systematically analyzes the reasons for the occurrence of a specific event, and thus analyzes the risk transmission and evolution process, but it is not widely used in large-scale modeling and analysis due to the cumbersome construction process; System Dynamics Theory, which explores the relationships within the system and between various elements by analyzing and studying information feedback, combining qualitative and quantitative methods, and presents the operation and behavior of the entire system through feedback loops; Bayesian Network, which is essentially a probabilistic inference network based on Bayesian conditional probability and graph theory, and realizes the inference of causal relationships between variables through the marginal independence and conditional dependence probability distributions of uncertain information.

[0003] Traditional methods rely mostly on general classification algorithms when dealing with the grouping of risk factors, and do not consider the problem of the balance of the group sizes of related risk factors. Therefore, problems such as parameter explosion and inaccurate distribution construction may occur in the actual process of constructing the joint distribution. In addition, in the existing research on risk scheduling and risk propagation in water network systems, there is less research on constructing the hierarchical structure of complex networks and the inter-layer mutual feedback associations, making it difficult to accurately locate risks in complex water network systems, and the different objects affected by risks directly determine problems such as the size and strength differences of the affected areas of the water network system. In summary, many limitations make the existing technology have certain deficiencies in the dynamic identification method of the risk evolution law of complex water network systems. Summary of the Invention

[0004] Object of the Invention: To provide a method for dynamically identifying the risk evolution law of complex water network systems to solve the above problems existing in the prior art.

[0005] Technical Solution: The method for dynamically identifying the risk evolution law of complex water network systems includes the following steps:

[0006] Step S1: Collect the basic information of water conservancy projects in the water network research area and identify risk factors to obtain a risk factor sample set;

[0007] Step S2: Divide the water conservancy projects in the water network research area into a hierarchical structure with three levels of outline, category, and junction that interact with each other to construct a multi-objective real-time risk scheduling model. Use the risk factor sample set as the input and solve it to obtain a set of risk scheduling solutions.

[0008] Step S3: Combine the set of risk scheduling solutions and establish a real-time scheduling risk propagation model for each level in view of the hierarchical structure of the complex water network system. Sequentially analyze the risk propagation mechanisms within each level of the outline, category, and junction, and establish a node dominance mapping between levels according to the water system connection relationship between levels to obtain a global real-time risk propagation network model.

[0009] Step S4: Based on the global real-time risk propagation network model, identify the vulnerable nodes and critical risk paths at the outline, category, and junction levels respectively, and perform a cross-level node dominance mapping on them to identify the vulnerable levels and critical risk paths of the entire water network system.

[0010] According to one aspect of the present application, the step S3 is further as follows:

[0011] Step S31: Read and establish a complex network for each level based on the hierarchical structure. Generalize the water conservancy projects at each level into nodes, and establish a directed edge between nodes with direct hydraulic connections.

[0012] Step S32: Analyze the differences in the number of nodes and the influence range at each level of the outline, category, and junction, and construct a risk propagation model for each level based on the complex network of each level.

[0013] Step S33: Based on the connection relationship of the water system between the upstream and downstream of the water network in the research area, construct a cross-level risk propagation mapping mechanism in which the nodes at the outline level map and dominate the nodes at the category level, and then the nodes at the category level map and dominate the nodes at the junction level, and construct a cross-level risk propagation network model.

[0014] According to one aspect of the present application, the step S32 is further as follows:

[0015] Step S32a: Establish a pressure wave propagation dynamics model for simulating risk propagation for the outline level, calculate the influence of each node failure, and sort them.

[0016] Step S32b: Establish a time-varying SIR model for the category level, divide the state of each node into a susceptible sub-state, an infected sub-state, and a recovered sub-state. At each moment, the sum of the weights of the sub-states of each node is 1.

[0017] Step S32c: Establish an asymmetric risk diffusion model for simulating risk propagation for the junction level, and the weight of the directed edge between nodes represents the risk conduction intensity.

[0018] According to one aspect of the present application, the step S4 is further as follows:

[0019] Step S41: Conduct intelligent local attacks and dynamic random attacks on the global real-time risk propagation network model to obtain the failure node sets at each level under the attacks. Through vulnerability quantification and propagation path discovery, obtain the vulnerable nodes and critical risk paths at each level.

[0020] Step S42: Based on the differences in risk occurrence between levels, set a level amplification factor to map the vulnerable nodes and critical risk paths between levels, and identify the vulnerable levels and critical risk paths of the entire water network system.

[0021] According to one aspect of the present application, step S41 is further as follows:

[0022] Step S41a: Calculate the node attack priority based on node topological attributes and dynamic weights, and preferentially attack the nodes whose node topological attributes are higher than the preset threshold to generate a local attack failure node set.

[0023] Step S41b: Adaptively adjust the attack frequency according to the real-time state of the network, randomly select nodes to inject attack traffic, and record the nodes whose failure ratio exceeds the critical value to generate a dynamic attack failure node set.

[0024] Step S41c: Integrate the local attack and dynamic attack failure node sets, calculate the node influence factor through the vulnerability quantification model, and combine with the propagation path discovery to obtain the vulnerable nodes and critical risk paths at each level.

[0025] According to one aspect of the present application, step S42 is further as follows:

[0026] Step S42a: Based on the hierarchical topological structure of the water network system, establish a risk transfer matrix to analyze the coupling effect between adjacent levels, and thereby set the risk amplification factor of the level.

[0027] Step S42b: Based on the level risk amplification factor, map the vulnerable nodes and critical risk paths of the level, and identify the vulnerable levels and critical risk paths of the entire water network system.

[0028] According to one aspect of the present application, step S1 is further as follows:

[0029] Step S11: Collect the basic information of water conservancy projects in the water network research area, identify the risk factors from it, and screen out the risk factor set.

[0030] Step S12: Read the risk factor set and use the spectral clustering method with balanced inter-group sizes to group the risk factor set. For each group of related and non-related risk factors, construct the risk factor distributions respectively, including the joint distribution of related risk factors and the distribution of non-related risk factors.

[0031] Step S13: Generate a sample set of risk factors based on the risk factor distribution, use the entropy-regularized Wasserstein optimal transport algorithm to obtain a spatiotemporally aligned mixed sample set, and test and correct it to obtain a risk factor sample set.

[0032] According to one aspect of the present application, in step S12, the spectral clustering method for balancing the group scale is specifically:

[0033] Based on the risk factor set, identify the associated risk factors and non-associated risk factors therein;

[0034] Set the group scale and the quantity constraint of the associated risk factors within the group, test and adjust the risk factors of the classification clusters to obtain the risk factor set grouping.

[0035] According to one aspect of the present application, step S2 is further:

[0036] Step S21: Divide the water conservancy projects in the water network research area into a hierarchical structure of three levels of outline, category, and node with mutual feedback to construct a multi-objective real-time risk scheduling model, where the outline level is major water diversion projects, the category level is river-lake connectivity projects and water transmission and distribution projects, and the node level is water conservancy hub projects such as reservoirs and pumping stations;

[0037] Step S22: Use the risk factor sample set as the input, map the objective functions of each level to the superposition state of quantum bits, establish the inter-level correlation through the entanglement mechanism, and generate a risk scheduling plan set.

[0038] According to one aspect of the present application, in step S21, the objective functions and constraint conditions of the multi-objective real-time risk scheduling model are specifically:

[0039] The outline level aims to minimize the water diversion risk, ecological impact, and economic cost, the category level aims to minimize the comprehensive risk, economic cost, and maximize the water supply benefit, and the node level aims to minimize the comprehensive risk, operation cost, and maximize the comprehensive income;

[0040] The constraint conditions include the water diversion capacity limit constraint and water volume balance constraint at the outline level, the project water transmission capacity limit constraint, hydraulic connection constraint, river channel ecological flow constraint, and water supply guarantee constraint at the category level, and the water volume balance constraint, equipment capacity constraint, hydraulic coupling constraint, and flood control control point safety constraint at the node level;

[0041] Based on the objective functions and constraint conditions of each level, construct a multi-objective real-time risk scheduling model.

[0042] According to one aspect of the present application, the specific outputs of the present invention include:

[0043] Vulnerable nodes and critical risk paths at each level of the outline, category, and knot in a complex water network system, as well as the vulnerable levels of the complex water network system and the main risk propagation paths of the overall system.

[0044] Beneficial effects: The spectral clustering method for balancing the scale between groups proposed by the present invention takes into account the balance between group scales and the correlation of factors within groups, and solves the deviation problem of traditional clustering algorithms in risk factor grouping. The dynamic fractal collaborative quantum optimization algorithm proposed to solve the complexity of multi-objective optimization problems uses quantum teleportation for instruction transmission between levels, achieves cross-layer response at the millisecond level, and reduces the complexity of the algorithm by compressing the solution space through the fractal dimension, which is applicable to the solution requirements of large-scale water network systems. In view of the scale, characteristics, and differences in the impact of risk occurrence of water conservancy projects in complex water network systems, a risk propagation model specific to each level is established, realizing the study of the risk propagation and evolution law of complex water network systems at different levels. At the same time, it provides an effective reference for accurately locating the risk levels, the main risk propagation paths, and the core control points and paths within the levels, and has high technological innovation and practical significance. Brief Description of the Drawings

[0045] Figure 1 It is a flowchart of the present invention.

[0046] Figure 2 It is a flowchart of step S1 of the present invention.

[0047] Figure 3 It is a flowchart of step S3 of the present invention. Detailed Embodiment

[0048] Taking a complex water network system in a certain basin as an example, the technical solution of the present invention will be described in detail below in conjunction with the drawings.

[0049] As Figures 1 to 3 shown, according to one aspect of the present application, a method for dynamically identifying the risk evolution law of a complex water network system is provided, which is characterized by including the following steps:

[0050] Step S1: Collect the basic information of water conservancy projects in the water network research area and identify risk factors, comprehensively rank the influence effects of risk factors using the multi-modal dynamic weight fusion and correction sorting method, screen to obtain a risk factor set, group the risk factor set using the spectral clustering method for balancing the scale between groups, construct distributions for the grouped risk factors respectively, and finally construct a risk factor sample set through the coupled optimization method of hierarchical hybrid sampling;

[0051] Step S2: Divide the water conservancy projects in the water network research area into a three - level hierarchical structure of outline, category, and node with mutual feedback. Based on the principles of each level, establish the objective function and constraints of each level, construct a multi - objective real - time risk scheduling model, use the risk factor set as the input, and solve it using the dynamic fractal collaborative quantum optimization algorithm to obtain the risk scheduling solution set of the complex water network system;

[0052] Step S3: Combine the risk scheduling solution set and establish real - time scheduling risk propagation models for each level of the complex water network system according to its hierarchical structure. Sequentially analyze the risk propagation mechanisms within each level of the outline, category, and node, and establish node dominance mappings between levels based on the water system connection relationships between levels to obtain the global real - time risk propagation network model;

[0053] Step S4: Based on the global real - time risk propagation network model, identify the vulnerable nodes and key risk paths at the outline, category, and node levels respectively, and perform cross - level node dominance mappings on them to identify the vulnerable levels and key risk paths of the entire water network system.

[0054] Traditional research on the risk laws of water network systems generally only considers the influence of single or several uncertain factors, with less consideration of comprehensive risk factors. Furthermore, there is a lack of much research reference for problems such as the curse of dimensionality and high computational complexity that may be caused by constructing the distribution of more risk factors. In addition, complex systems usually involve a wide range of objects and are large - scale, with different characteristics within the object group. There are great difficulties in organizational and computational aspects for comprehensive analysis of their risk evolution laws, and there is a lack of strong prioritization in the analysis of risk characteristics, making it impossible to put into production practice for targeted risk regulation and other issues.

[0055] In the present invention, many uncertainties involved in the complex water network system are comprehensively considered, and at the same time, risk factors with higher sorting priorities are selected to avoid the influence of unimportant factors on the analysis effect. Considering the impact of a large number of risk factors on the calculation speed and efficiency, after screening out associated factors and non - associated factors, a spectral clustering method for balancing the group sizes is proposed to group the risk factor set, taking into account the balance of group sizes and the relevance of factors within the group, and solving the deviation problem of traditional clustering algorithms in risk factor grouping. In the sampling stage based on the risk factor distribution, a coupled optimization method of hierarchical hybrid sampling is proposed, taking into account the joint distribution of associated risk factors and the independent distribution of non - associated risk factors, and coupling the two considering the influence of spatio - temporal factors, ensuring the sampling accuracy and efficiency.

[0056] The complex water network system is huge in scale, and there are complex hydraulic connections among the water conservancy projects in the water network research area, making it difficult to directly construct a real-time risk scheduling model. In the present invention, it is considered to divide the water network system into a three-level hierarchical structure of "outline, category, and node" according to the scale and characteristics of water conservancy projects. The water conservancy projects within and between the levels are closely related, ensuring the possibility of establishing a risk scheduling model for the complex water network system. In addition, the water network system usually has multiple objectives during operation. In the research of the present invention, the objective functions of each level are established by comprehensively considering the criteria of each level, and a multi-objective optimization problem of collaborative optimization and solution of the three-level objective functions is established. At the same time, a dynamic fractal collaborative quantum optimization algorithm is proposed to solve the complexity of solving the multi-objective optimization problem. Quantum teleportation is used for instruction transmission between levels, achieving cross-layer response at the millisecond level, and reducing the algorithm complexity by compressing the solution space through the fractal dimension, which is applicable to the solution requirements of large-scale water network systems. In addition, the established dynamic balance entropy mechanism combines quantum annealing and classical entropy indicators to solve the stability problem in the screening of multi-objective solution sets.

[0057] In the research on the law of risk propagation, the complex network theory is applied to establish the complex networks of each level respectively, realizing the graphical combination of the water network topological structure and the analysis of the law of risk propagation, and laying a foundation for the analysis of the law of risk propagation. Considering the characteristic differences in the number of nodes between different levels and the scope of risk influence in the water network system, risk propagation models of each level are established specifically to simulate the risk evolution within the level; in addition, based on the connection relationship of the water systems between the upstream and downstream, a risk propagation mechanism between levels is established. Thus, a new research method and example are provided for the analysis of the law of risk propagation in the complex water network system.

[0058] Based on the risk propagation model, the vulnerability of the water network system is quantified by using the methods of intelligent local attack and dynamic random attack simulation, the vulnerable nodes and key risk paths of each level are identified, and amplification coefficients of each level are set based on the difference in the influence effect between risk levels for risk mapping between levels, obtaining the vulnerability levels and key risk paths of the entire system, which is conducive to carrying out targeted risk regulation work on the water network system.

[0059] According to one aspect of the present application, step S1 is further as follows:

[0060] Step S11: Collect the basic information of the water conservancy projects in the water network research area, and identify risk factors by using the comprehensive method of brainstorming - literature mining - reduced-round Delphi; based on the risk factor data, conduct sorting and preprocessing to obtain a multi-modal data set and calculate the multi-modal fusion eigenvalue of the risk factors; rank the risk factors based on the multi-modal fusion eigenvalue, correct the ranking by using an exponential spatio-temporal decay kernel function, and select the ranked risk factors by using the Pareto analysis method to obtain a risk factor set;

[0061] In this embodiment, the required basic information can be collected from public data. The basic information of water conservancy projects mainly includes hydrology, geology, and project operation data. The data types include numerical data, text data, and spatio-temporal data, so as to achieve the purpose of deeply understanding the basic situation and hydrological characteristics of the water network research area, and provide basic information and data support for subsequent model design and construction, etc.

[0062] According to one aspect of the present application, in the step S11, the specific steps for calculating the multi-modal fusion eigenvalue of the risk factor are as follows:

[0063] Sort the risk factor data according to numerical, text, and spatio-temporal types, and preprocess the sorted data respectively. The numerical data is normalized, the text data is segmented and vectorized, and the spatio-temporal data is rasterized, spatially interpolated, and time-aligned, thereby obtaining the multi-modal datasets of risk factors in numerical modality, text modality, and spatio-temporal modality;

[0064] Based on the preprocessed multi-modal datasets of risk factors, extract the modal features respectively. The numerical modality uses the time series feature extractor Transformer to extract trend, period, and outlier features, the text modality uses the pre-trained language model BERT to extract semantic features, and the spatio-temporal modality uses the spatio-temporal Transformer to extract spatial dependence and time evolution features;

[0065] Set the initial weights of numerical, text, and spatio-temporal modalities based on expert experience, use the Choquet fuzzy integral to fuse the multi-modal features, apply the game model to dynamically update the weights of each modality based on the strategy of maximizing the rationality of the overall ranking by adjusting its own weights, and use the gradient descent method to iteratively optimize the modal weights to obtain the multi-modal fusion eigenvalue of the risk factor.

[0066] In this embodiment, the risk factors identified by the brainstorming-literature mining-round-reduced Delphi comprehensive method are extensive, so the method of multi-modal dynamic weight fusion and correction ranking is used to screen the risk factors.

[0067] Firstly, the collected basic data of risk factors are sorted out, and divided into numerical data, text data and spatiotemporal data according to the information type. The numerical data mainly includes time series data of reservoirs, sluice pumps, pumping stations, channels, etc. The text data mainly includes engineering logs, expert reports and historical disaster records, etc. The spatiotemporal data mainly includes river distribution in geographic information systems, the location of reservoirs, etc.; then the data are preprocessed separately, the numerical data is normalized, the text data is segmented and vectorized, and the spatiotemporal data is rasterized, spatially interpolated and time-aligned, thereby obtaining a multimodal data set of risk factors under numerical mode, text mode and spatiotemporal mode; based on the preprocessed multimodal data set of risk factors, modal features are extracted respectively. The numerical mode uses the time series feature extractor Transformer to extract trend, cycle and anomaly features, the text mode uses the pre-trained language model BERT to extract semantic features, and the spatiotemporal mode uses the spatiotemporal Transformer to extract spatial dependency and time evolution features; based on expert experience, an initial weight ω is assigned to each mode i In this embodiment, the numerical mode ω1=0.4, the text mode ω2=0.3, and the spatiotemporal mode ω3=0.3 (ω1+ω2+ω3=1); Choquet fuzzy integral is used to fuse multimodal features. First, the fuzzy measure is defined for each modal subset. S Included in {value, text, time and space}, define the weight μ(S), satisfying: μ(S1∪S2)≧μ(S1)+μ(S2)-μ(S1∩S2), using Choquet integral calculation, the formula is expressed as: F(x)=∑ n i=1 {[h(x i )-h(x i-1 )]·ω(Ai)}, where h ( x (i) ) is the i The eigenvalues of the modes (in ascending order), ω ( A i ) is the front i The joint weight of each mode can capture the interaction between modes by using the fuzzy integral method, avoiding the problem that the traditional linear weighting method ignores the nonlinear relationship; the game model is constructed based on the strategy of adjusting its own weight to maximize the rationality of the overall sorting, with the three modes of value, text and time and space as "players", and the profit function is defined based on the Kendall Tau correlation coefficient τ, and the expression formula is:

[0068] income i =τ(model ranking, expert ranking)-λ·丨ω i -ω i 初始丨, where λ is the weight change penalty function, and the gradient descent method is used to iteratively optimize and update the weights of each modality until the strategies of each modality are stable. The formula is: ω i t+1 =ω i t +η·dConsistency / dω i , where η is the learning rate, which is used to control the speed of weight adjustment; the benefit i represents the benefit value of the i-th mode; τ represents the ranking consistency measure; model ranking refers to the ranking result generated by the algorithm; expert ranking refers to the ranking result manually annotated; ω i is the current modal weight; ω i 初始 is the initial weight value; dConsistency / dω i represents the partial derivative of the consistency index with respect to the weight; t represents the number of iterations. d represents the partial derivative.

[0069] In this way, the multimodal fusion characteristic values of the risk factors are obtained, and the risk factors are arranged in descending order according to the multimodal fusion characteristic values; finally, the exponential spatiotemporal attenuation kernel function is used to reduce the ranking of risk factors with a long history and a long spatial distance, and the Pareto analysis method is used to select the top 80% of the risk factors after sorting as the risk factor set.

[0070] In this embodiment, multi-source information is jointly represented with the help of multi-modal learning in computer vision and natural language processing to enhance the complementarity between information and expand the utilization of water network information in the study area; then the fuzzy integral method is used to enhance the processing of non-additive weights and realize the fusion of multi-modal data; numerical values, texts, and spatiotemporal modalities are regarded as game participants respectively, and the ranking of risk factors is obtained through the Nash equilibrium optimization weight allocation strategy; finally, the ranking results are optimized and the top 80% are selected to form a risk factor set. Therefore, compared with the drawbacks of traditional fixed weights and isolated processing of multi-modal data, a multi-modal dynamic weight fusion correction sorting method that uses comprehensive fuzzy integrals, game models, and expert evaluation feedback embedded in the game payoff function is adopted to achieve the effect of real-time response to data changes and integration of cross-modal collaboration.

[0071] Step S12, reading the risk factor set, identifying the associated risk factors and the unassociated risk factors, and grouping the risk factor set using the spectral clustering method with balanced inter-group scale, constructing the joint distribution of the associated risk factors using the adaptive unit joint distribution, optimizing the distribution type using the Bayesian information criterion and performing a goodness of fit test, and obtaining the distribution of the unassociated risk factors;

[0072] In the water network research area, the number of risk factors obtained through screening is relatively large. There are problems such as the curse of dimensionality, high computational complexity, and error accumulation when directly establishing a joint distribution for the relevant risk factors. In this embodiment, to solve this problem, a spectral clustering method for balancing the group sizes is proposed to group the risk factor set, aiming to control the scale of the relevant risk factors within each group.

[0073] According to one aspect of the present application, step S12 is further as follows:

[0074] Step S12a: Construct a hypergraph model based on the risk factors, with the risk factors as hypergraph nodes, and construct initial state hyperedges according to the node information. Define the cross-entropy loss function and use the gradient descent method to optimize and update the hyperedge weights through backpropagation; screen the risk factor nodes with hyperedge weights exceeding the threshold as relevant risk factors, and this threshold is determined by the cross-entropy loss;

[0075] Step S12b: Based on the identified relevant risk factor set and non-relevant risk factor set, calculate the conditional mutual information and perform a permutation test to generate a sparse correlation matrix; construct a normalized Laplacian matrix based on the correlation matrix, solve the eigenvector mapping through semi-definite programming to generate a low-dimensional embedding space and the scattered distribution of the strongly correlated factors in the embedding space; use a capacity-sensitive greedy algorithm in the embedding space to obtain the grouping of the risk subsets;

[0076] Step S12c: Construct a multi-dimensional joint distribution space based on the relevant risk factors, perform an initial partition using a density-based spatial clustering method, optimize the distribution unit boundaries in combination with the information entropy constraint criterion, test the homogeneity of the data within the unit through the KL divergence, construct the local probability density function of each unit using kernel density estimation, and finally fuse the marginal distribution and the dependence structure through the Copula function to establish a non-parametric joint distribution;

[0077] Step S12d: Initially screen the candidate distributions according to the data characteristics of the non-relevant risk factors, gradually fit the candidate distributions using the EM algorithm and estimate the parameters, select the optimal distribution type based on the Bayesian information criterion, and perform a goodness-of-fit test using the K-S test to obtain the distribution and parameters of the non-relevant risk factors.

[0078] In this embodiment, first construct a hypergraph model to divide the risk factor set into a relevant risk factor set and a non-relevant risk factor set. Use the risk factors within the group as hypergraph nodes and construct initial state hyperedges based on the risk factor information. The formula for the defined cross-entropy loss function is as follows:

[0079] L =-∑ e∈E [p true (e)·log(p model (e))+(1-p true(e)·log(1 - p model (e)].

[0080] Wherein, L represents the sum of all hyper - edge cross - entropy losses, that is, the total loss; p true ( e ) represents the frequency of the hyper - edge e appearing in historical events (normalized to probability), p model ( e ) = σ(ω e ) represents the hyper - edge weight ω e The probability after being mapped by the Sigmoid function; after defining the cross - entropy loss function, the hyper - edge weights are updated by backpropagation through the gradient descent method, which improves the model's ability to express complex association patterns. The formula of the gradient descent method is as follows: ω e t+1 = ω e t - η·dL / dω e ; wherein, η is the learning rate, and dL / dω e represents the partial derivative of the total loss with respect to the hyper - edge weight; finally, a threshold dynamically adjusted by the cross - entropy loss function is set to screen the risk - factor nodes whose hyper - edge weights exceed the threshold, and determine them as risk factors with significant relevance. This process avoids human - set biases through the adaptive threshold mechanism and ensures the statistical significance of the screening results.

[0081] Group the risk - factor set based on the principles of between - group size consistency and between - group uniformity of association factors. First, quantify the direct relevance between risk factors based on conditional mutual information (CMI), determine the significance threshold through permutation testing (set the threshold λ = 0.3 in this embodiment), generate a sparse association matrix A, only retain the significantly associated edges (CMI>λ), add repulsive - edge constraints to low - association factor pairs (CMI<0.1), and force them not to be assigned to the same group; construct a normalized Laplacian matrix based on the association matrix L m = D -1 / 2 ( D - A ) D -1 / 2 Structural basis, wherein L m represents the normalized Laplacian matrix, D represents the degree matrix; Next, construct the objective function and constraint conditions of balanced spectral clustering: min Y {Tr(Y T L m Y)}, s.t. Y T ·Y = Ik , for any i, ||Y i ||0 ≤ s max . In the formula, Y ∈ R n×k represents the clustering indicator matrix, I k represents the identity matrix, s max represents the maximum capacity of a single group (s max = ⌈n / k⌉ + δ, δ is the tolerance threshold), and then a semidefinite programming is used to solve this constrained eigenvalue problem, and the first k eigenvectors are extracted to map the original data to a low-dimensional embedded space. In this space, the strongly associated factors are naturally dispersed by the orthogonality constraint of the Laplacian matrix, avoiding the problem of the curse of dimensionality caused by the excessive concentration of the associated risk factors in a certain group. Finally, the weighted k-means algorithm is used to initialize the clustering centers in the low-dimensional embedded space to ensure the balanced geographical distribution of the initial grouping. For the groups exceeding the capacity limit, calculate their associated overlap degree with the neighboring groups:

[0082] ρ = ∑ i∈Gp,j∈Gq A ij / sqrt(|Gp||Gq|). In the formula, ρ represents the associated overlap degree, Gp represents the currently processed group, and Gq represents the neighboring group compared with Gp; when ρ > 0.7, the highly overlapping groups are merged, and then the redundant factors are redistributed to the neighboring group with the weakest association by the capacity-sensitive greedy algorithm, and finally the scale difference between groups is controlled within 20%. Thus, the balance of the within-group association strength and the grouping uniformity is achieved through the above method, providing a better input for the subsequent joint probability distribution modeling.

[0083] For the associated risk factors, a density-based spatial clustering is used to perform an initial partitioning of the multi-dimensional data, and the information entropy constraint criterion is combined to optimize the distribution unit boundary to ensure the data homogeneity within the unit (verified by the KL divergence test). The kernel density estimation is used for each distribution unit to construct a local probability density function, and the Copula function is used to fuse the marginal distributions and dependence structures of each unit, and finally a non-parametric multi-dimensional joint distribution model is established. This method avoids the strong assumptions of the traditional parametric distribution on the data form and improves the generalization ability of the model. For the non-associated risk factors, the candidate distributions are initially screened according to their data characteristics such as skewness and kurtosis, including the normal distribution, Weibull distribution, generalized Pareto distribution, etc. The EM algorithm is used to gradually fit the distribution parameters, and the optimal type is selected from the candidate distributions based on the Bayesian information criterion, and the goodness of fit of the distribution is verified by the K-S test. Finally, the distribution type and parameters of the non-associated risk factors are determined.

[0084] In summary, in this embodiment, through spectral clustering and hypergraph models that balance the group sizes, the balance of group sizes and the correlation of factors within the group are taken into account, and the offset problem of traditional clustering algorithms in risk factor grouping is solved. By combining the cross-entropy loss function and the gradient descent method, the dynamic adjustment of the screening threshold of correlation factors is realized, and problems such as possible overfitting of the model caused by manual intervention are reduced. Finally, by fusing non-parametric kernel density estimation and the Copula function, the non-linear dependence structure of complex risk factors can be effectively characterized, and the robustness of the joint distribution establishment of correlation risk factors is improved. In short, in this embodiment, through multi-stage optimization and statistical tests, the efficient modeling of high-dimensional risk factors and accurate risk quantification are realized.

[0085] Step S13: Generate a sample set of risk factors according to the risk factor distribution, use the entropy-regularized Wasserstein optimal transport algorithm to obtain a spatio-temporally aligned mixed sample set, and perform inspection and correction to obtain a risk factor sample set.

[0086] According to one aspect of the present application, the step S13 is further as follows:

[0087] Step S13a: Based on the joint distribution of correlation risk factors, use a hybrid method of reversible neural network and Hamiltonian Monte Carlo to obtain a sample set of correlation risk factors;

[0088] Step S13b: Based on the distribution and parameters of non-correlation risk factors, use the quantum state discretization and Grover search acceleration method to obtain a sample set of non-correlation risk factors;

[0089] Step S13c: Based on the sample set of correlation risk factors and the sample set of non-correlation risk factors, use the entropy-regularized Wasserstein optimal transport algorithm to process the spatio-temporal distribution differences between the sample sets to obtain a spatio-temporally aligned mixed sample set;

[0090] Step S13d: Calculate statistical indicators such as KL divergence, HSIC dependence strength, and extreme event coverage rate to test the mixed samples, and use the online feedback control and local resampling mechanism to correct the errors to obtain a risk factor sample set.

[0091] In this embodiment, by innovatively integrating the classical-quantum hybrid algorithm with the dynamic optimization mechanism, the problem of cross-time-space and multi-dimensional sampling of complex risk factors is solved. For correlated risk factors, through the hybrid method of reversible neural network and Hamiltonian Monte Carlo, accurate sampling is achieved in the high-dimensional non-linear joint distribution, taking into account the integrity of the distribution characteristics and the computational efficiency; for uncorrelated factors, quantum state discretization and Grover search acceleration algorithm are adopted, which breaks through the efficiency bottleneck of classical discretization to a certain extent and reduces the sampling complexity of large-scale sparse distributions. Based on the entropy-regularized Wasserstein optimal transport algorithm, the spatio-temporal distribution differences of samples are intelligently eliminated, the spatio-temporal coupling characteristics of risk factors are maintained, and a quality assessment system is constructed through multi-dimensional statistical tests such as KL divergence and HSIC. Combining the online feedback control and local resampling mechanism, key indicators such as the extreme event coverage rate are dynamically corrected to ensure that the sample set reaches the optimal balance between statistical significance and risk coverage completeness. Generally speaking, this step provides a sampling modeling method with high fidelity and high efficiency, and improves the quantitative analysis accuracy of complex risk systems.

[0092] According to one aspect of the present application, the step S2 is further as follows:

[0093] Step S21: Divide the water conservancy projects in the water network research area into a three-level hierarchical structure of outline, item, and node with mutual feedback to construct a multi-objective real-time risk scheduling model, where the outline level is major water diversion projects, the item level is river-lake connectivity projects and water transmission and distribution projects, and the node level is water conservancy hub projects such as reservoirs and pump stations;

[0094] In this embodiment, the scale of the complex water network system in a certain basin is large, and there are complex hydraulic connections among the water conservancy projects in the water network research area, making it difficult to construct a real-time risk scheduling model. Therefore, it is proposed to divide it into a three-level hierarchical structure of outline, item, and node according to the attribute characteristics and scale of the water conservancy projects in the water network research area. The water conservancy projects at the outline level include a certain river section and a certain river-XX River water diversion project, the water conservancy projects at the item level include a certain main canal system, a certain river main stream - a certain ecological water replenishment channel, and an A-B water transmission channel, and the water conservancy projects at the node level include a certain reservoir, XX reservoir, etc., as well as an XX sluice pump station group and an XX flood control project.

[0095] Based on the three - level division of the water network research area, combined with the principle of fractal self - similarity and the hydraulic connection between the upstream and downstream of water conservancy projects, the water network system is decoupled into three decision - making dimensions: the fractal main dimension at the class level as the macro - topological optimization level, the fractal secondary dimension at the order level as the meso - path planning, and the fractal primitive dimension at the node level as the micro - node regulation. A dynamic mutual - feedback mechanism between levels is established. This dynamic mutual - feedback mechanism consists of a forward instruction flow, a reverse information flow, and a horizontal coordination mechanism. Among them, the forward instruction flow means that information is transmitted from the class level to the order level and finally reaches the node level to get a response. The reverse information flow means the process that information is conducted from the node level, transmitted reversely through the order level to the class level. The horizontal coordination mechanism takes the order level as the conduction core, and the information is propagated up to the class level and down to the node level, thus forming a complex water network system with dynamic multi - level mutual - feedback. On the one hand, the hierarchical division makes the structural levels of the complex water network system clear. The risk impact effects and scopes within the same level are similar, and there are obvious differences between different levels, which is convenient for the accurate positioning of risk analysis. On the other hand, the connection between levels is established through the inherent upstream - downstream hydraulic connection of the water network system, which is different from the connection between levels of general complex systems. It makes the three levels have both the independence of research and close correlation, and will not form isolated levels, which is of great significance for the research of complex water network systems.

[0096] According to one aspect of the present application, in step S21, the multi - objective real - time risk scheduling model is specifically:

[0097] Class level: Taking the minimum of water transfer risk, ecological impact, and economic cost as the goal, it is expressed as:

[0098] F 纲 =g1 R 调水 +g2 R 生态 +g3 C 经济 ;

[0099] Among them, R 调水 =∑ n i=1 g i r i ; R 调水 represents the water transfer risk, and the weight is determined by the entropy weight method; R 生态 is the ecological impact quantification value, C 经济 is the investment and operation and maintenance cost of the water transfer project, and g1, g2, g3 are weights assigned by expert scoring, satisfying g1 + g2 + g3 = 1;

[0100] The constraints at the class level include the water transfer capacity limit constraint and the water volume balance constraint, which are expressed as:

[0101] Water transfer capacity limit constraint: ∑ n i=1 Q 调,i ≤Qmax;

[0102] In the formula, Q max represents the maximum water transfer capacity of the system;

[0103] Water volume balance constraint: ∑Q 入 -∑Q 出 =ΔS;

[0104] In the formula, Q 入 is the input or transferred-in water volume, Q 出 is the outflow or transferred-out water volume, Δ S represents the regional water volume change;

[0105] Objective level: Aiming at minimizing comprehensive risk, economic cost and maximizing water supply benefit. Among them, the comprehensive risk mainly includes flood control risk, flow interruption risk, ecological risk and water supply risk, expressed as:

[0106] F 目 =m1 R 综合 +m2 C 经济 -m3 B 供水 ; Among them, R 综合 =∑ 4 j=1 w j r j (flood control risk r1, flow interruption risk r2, ecological risk r3, water supply risk r4);

[0107] B water supply = ∑ m k=1 q k p k (water supply benefit, q k is the water supply volume, p k is the water supply unit price); m1, m2, m3 are the weights assigned by expert scoring, satisfying m1 + m2 + m3 = 1;

[0108] The constraint conditions at the objective level include engineering water conveyance capacity limit constraint, hydraulic connection constraint, river ecological flow constraint, water supply guarantee constraint, expressed as:

[0109] Engineering water conveyance capacity limit constraint: Q k (t)≤Q cap,k , for any k ∈ engineering node;

[0110] Hydraulic connection constraint: H i (t) = f ( Q i (t)), for any i ∈ river channel nodes;

[0111] River channel ecological flow constraint: Q 生态,j (t) ≥ Q min,j , for any j ∈ ecologically sensitive cross-sections;

[0112] Water supply guarantee constraint: ∑ m k=1 q k （t） ≥ D 需，t ;

[0113] Hierarchy: Aiming at minimizing comprehensive risk, operation cost and maximizing comprehensive benefit, where the comprehensive risk mainly includes flood control risk, water supply shortage risk, structural safety risk, ecological risk and power generation shortage risk, and the comprehensive benefit mainly includes power generation benefit, water supply benefit and ecological benefit, expressed as:

[0114] F 结 = j1 R’ 综合 + j2 C 运行 - j3 B 综合 ;

[0115] Among them, R’ 综合 = ∑ 5 l=1 w l ’ r l ’ (flood control risk r1’, water supply shortage risk r2’, structural safety risk r3’, ecological risk r4’, power generation shortage risk r5); B 综合 = B 发电 + B 供水 + B 生态 (The power generation benefit is calculated based on the electricity price and power generation volume, and the ecological benefit is quantified according to the restoration effect); j1, j2, j3 are weights assigned by expert scoring, satisfying j1 + j2 + j3 = 1;

[0116] The constraint conditions at the knot level include water balance constraint, equipment capacity constraint, hydraulic coupling constraint, and flood control control point safety constraint, which are expressed as:

[0117] Equipment capacity constraint: P 发电,i (t) ≤ P rated,i , for any i ∈ hydropower station;

[0118] Flood control control point safety constraint: H 防洪,j (t) ≤ H 安全,j , for any j ∈ flood control control point;

[0119] Hydraulic coupling constraint: Q 上游 ( t ) = Q 下游 ( t ) + Δ Q 分流 ( t );

[0120] Based on the objective function and constraint conditions at the outline, category, and knot levels, a multi-objective real-time risk scheduling model for complex water network systems is constructed.

[0121] Step S22: Using the risk factor sample set as the input, map the objective functions at each level to the superposition state of quantum bits, establish the correlation between levels through the entanglement mechanism, and generate a set of risk scheduling schemes;

[0122] According to one aspect of the present application, the step S22 is further as follows:

[0123] Step S22a: Map the objective functions at the outline, category, and knot levels to the superposition state of quantum bits, where the objective functions at the outline, category, and knot levels are respectively encoded as high, medium, and low-level quantum bits; realize the entanglement of quantum bits at the three levels through quantum gate operations to form an overall state to achieve the correlation between levels, and any change in the state of any level will affect the states of other levels through the defined entanglement mechanism;

[0124] Step S22b: Through the correlation of the entangled state, compress the solution spaces at the outline, category, and knot levels into an overall space, use the improved quantum particle swarm optimization algorithm to adjust the particle positions in the solution space, and use non-dominated sorting and crowding degree calculation to screen and retain the elite solutions to obtain a set of risk scheduling schemes for complex water network systems;

[0125] Traditional multi-objective optimization algorithms have the problem of low computational efficiency. Classical algorithms such as NSGA-II and MOPSO need to traverse a huge solution space. Due to the large scale of the water network system, the calculation time will increase exponentially with the scale of the water network, making it difficult to meet the needs of risk scheduling research for the water network system. In addition, the established multi-objective risk scheduling model with multi-level dynamic mutual feedback may have multiple local optimal solutions, and general multi-objective optimization algorithms are prone to falling into local optima; moreover, traditional algorithms are mostly static optimizations and lack an information transmission mechanism between dynamic levels. Therefore, this study proposes a quantum particle swarm optimization algorithm integrated with dynamic fractal cooperation, which has better global search ability and faster convergence efficiency through parallel computing, quantum superposition, and entanglement.

[0126] In this embodiment, the specific implementation steps are as follows: First, perform quantum encoding, map the objective functions of each level of the outline, item, and node into the superposition state of quantum bits. The objective of the outline level is encoded as high-order quantum bits, the objective of the item level is encoded as middle-order quantum bits, and the objective of the node level is encoded as low-order quantum bits; then, perform the adaptation of the fractal dimension. Specifically, through the self-similarity of fractal geometry, the global optimization problem is recursively decomposed into sub-problems, and each sub-problem corresponds to a sequence of quantum gate operations.

[0127] Implement a dynamic mutual feedback transmission mechanism between levels through quantum teleportation channels. Specifically, the outline level sends optimization instructions to the item level by transmitting the probability amplitude distribution of the optimal solution through quantum teleportation technology, avoiding the delay problem of traditional communication to a certain extent; the real-time state of the node level is fed back to the item level through quantum measurement, triggering the dynamic adjustment of the parameters of the item level, and the expression form is:

[0128] β new = βe -γ‖ΔQnode‖ ; In the formula, β is the original weight coefficient of the item level, β new is the adjusted weight coefficient, Δ Q node is the node flow deviation, and γ is the attenuation coefficient.

[0129] In the process of co-evolution of quantum particle swarms, each particle represents a solution of a fractal level combination, and its position is described by a quantum state, expressed as: |ψ>=α|0>+β|1>;

[0130] Then, adopt the following update rule to integrate the quantum rotation gate and the classical PSO speed update, expressed as: v id t+1 =w·v id t +c1·R(θ pbest )+c2·R(θ gbest );

[0131] In the formula, R (θ) is the quantum rotation gate operation, which is used to adjust the phase of the quantum state to approximate the Pareto front. Using the quantum annealing filter, the Pareto solution set is input into the quantum annealer, and the system entropy minimization is used as the objective function. Thus, the risk scheduling scheme set that takes into account both stability and efficiency is screened and expressed as:

[0132] S opt = argmin Si {(-∑pi ln(pi)) + λ Risk Index}; In the formula, p i is the flow distribution probability of the scheme S i . Risk Index represents the risk index. v id t represents the velocity of the i-th particle in the d-th dimension at the t-th iteration; v id t+1 represents the updated velocity; w represents the inertia weight; c1 and c2 represent the learning factors; θ pbest represents the rotation angle corresponding to the individual optimal position; θ gbest represents the rotation angle corresponding to the global optimal position; S opt represents the optimal scheme set. λ is the balance coefficient.

[0133] In summary, in this embodiment, a quantum-classical hybrid architecture is constructed, and quantum teleportation is used for instruction transmission between layers, achieving cross-layer response at the millisecond level, which has a certain improvement in timeliness compared with the traditional NSGA-II method. Through the fractal-quantum coupling modeling method that compresses the solution space by the fractal dimension, the algorithm complexity is reduced from O (n 3 ) to O (nlogn), which is applicable to large-scale water network systems. In addition, the established dynamic balance entropy mechanism combines quantum annealing and classical entropy indicators to solve the stability problem in the screening of multi-objective solution sets.

[0134] According to one aspect of the present application, the step S31 is further:

[0135] Step S31: Read and establish a complex network for each layer based on the hierarchical structure, generalize the water conservancy projects of each layer into nodes, and establish a directed edge between the nodes with direct hydraulic connections;

[0136] Step S32: Analyze the differences in the number of nodes and the influence range in each level of the outline, category, and conclusion, and construct a risk propagation model for each level based on the complex network of each layer;

[0137] Step S33: Based on the connection relationship of the water systems between the upstream and downstream of the water network in the study area, construct a cross-level risk propagation mapping mechanism in which the nodes at the class level map and dominate the nodes at the order level, and then the nodes at the order level map and dominate the nodes at the knot level, and build a risk propagation network model across levels.

[0138] In this embodiment, first, complex networks at each level of class, order, and knot are constructed. The water conservancy projects within each divided level are used as nodes, and directed edges are established between the nodes with direct hydraulic connections, realizing the combination of complex network theory and water conservancy topological structure, and laying a foundation for the establishment of the water network system risk propagation model and the analysis of risk propagation characteristics. Based on the distinct characteristics of the complex networks constructed at each level of the water network, where the number of nodes at the class level is small but the reachability of the node risks in the water network is relatively wide, the number of nodes at the knot level is relatively large but the influence range of the node risks in the water network is significantly small, and the above two characteristics of the order level are relatively intermediate, risk propagation models at each level are established accordingly. In addition, considering the relevance of risks at each level, analyze the cross-level risk propagation mechanism and establish a cross-level risk propagation model.

[0139] According to one aspect of the present application, the step S32 is further as follows:

[0140] Step S32a: Based on the characteristics that the number of nodes at the class level is small but the influence range of the nodes is wide, establish a pressure wave propagation dynamics model to simulate the risk propagation at the class level, set the node pressure deviation threshold, and calculate and sort the failure influence of each node through the cascading failure propagation algorithm and the improved PageRank algorithm;

[0141] Step S32b: Establish a time-varying SIR model for the order level, divide the state of each node into a susceptible sub-state, an infected sub-state, and a recovered sub-state, and at each moment, the sum of the weights of the sub-states of each node is 1;

[0142] Step S32c: Generalize the nodes of the constructed complex network at the knot level into multi-dimensional state vectors, and define the weight of the directed edge between nodes to represent the risk conduction intensity; use the fuzzy comprehensive evaluation method to calculate the node risk entropy, and establish an asymmetric risk diffusion model to represent the risk propagation of the nodes at the knot level.

[0143] In this embodiment, on the basis of constructing complex networks at each level of class, order, and knot, establish risk propagation dynamics models to simulate the risk propagation within and between each level, providing an effective reference for identifying the risk evolution law of the water network system.

[0144] Based on the characteristics that the number of nodes at the class level is relatively small but the risk situation of each node is likely to have a greater impact within the scope of the water network study area, establish a pressure wave propagation dynamics model to simulate the diffusion of risks at the class level. On the basis of the nodes and directed edges of the complex network constructed at the class level, construct a weighted adjacency matrixW ( t ), where the element w ij ( t ) represents the risk propagation intensity of the node i to j , expressed as:

[0145] w ij (t) = Q ij (t) / Q design × e -λL ij / v(t) × (1 + 0.2 C B ( j ));

[0146] In the formula: Q ij (t) / Q design represents the flow load rate, e -λL ij / v(t) represents the time-delay attenuation term, (1 + 0.2 C B ( j )) represents the hub enhancement factor. In addition, λ takes 0.15 s -1 represents the empirical attenuation coefficient, C B ( j ) is j the betweenness centrality of the node, reflecting the hub degree of the node in the network, and is normalized to [0, 1] here. Establish the water hammer effect control equation and solve the transient flow equation using the method of characteristics, which is expressed as follows:

[0147] dH / dt + (c 2 / gA)·dQ / dx = 0; dQ / dt + gA·dH / dx + f Q|Q| / (2DA) = 0;

[0148] Among them: H ( x , t ) represents the piezometric head; c = (K / ρ) 0.5 / (1 + (K / E)(D / e)) 0.5 is the water hammer wave speed, K is the bulk modulus of the fluid, E is the elastic modulus of the pipe, D is the inner diameter of the pipe, and e is the wall thickness of the pipe; f is the Darcy - Weisbach friction coefficient. Construct the risk pressure fluctuation equation and define the node risk pressure fluctuation quantityP i ( t ) is expressed as follows:

[0149] Pi(t) = α·|(Hi(t)-H design ) / (H fail -H design )| + β·(dQi / dt) / Q max ;

[0150] Where: Pi(t) represents the risk pressure fluctuation of node i at time t; Hi(t) represents the water head of node i at time t; H design represents the design water head; H fail represents the failure water head (the critical water head value at which the pipeline may fail); dQi / dt represents the change rate of the flow rate at node i; Q max represents the maximum flow rate; α and β are weight coefficients, representing the contribution ratios of water head deviation and flow rate change rate to risk assessment respectively. α = 0.7, β = 0.3 are the weight coefficients.

[0151] Establish a cascading failure propagation mechanism. First, set the node failure trigger conditions. If any condition is met, the node i will trigger a failure, which is expressed as follows:

[0152] Condition 1: P i (t)>1.2 P threshold ;

[0153] Condition 2: There exists j ∈U( i ), dP j / dt >0.5s -1 and C B ( i )>0.8;

[0154] In the formula, U ( i ) is the set of upstream nodes of node i .

[0155] Monitor the P i (t) of each node in real time. After any failure condition is triggered, it will be marked as the failure state, and the pressure redistribution calculation will be performed, which is expressed as follows:

[0156] ΔP prop = ∑ j∈Di w ji(t) (P j (t)-P threshold ) / (1+e-0.1t );where \(D(i)\) is the set of direct downstream nodes of node \(i\). \(\Delta P_{prop}\) represents the risk pressure propagation amount; \(j\in D_i\) means that node \(j\) belongs to the set of direct downstream nodes of node \(i\); \(w\) ji(t) represents the influence weight of node \(j\) on node \(i\) at time \(t\); \(P\) j (t) represents the pressure value of node \(j\) at time \(t\); \(P\) threshold represents the pressure threshold; \(e\) -0.1t represents an exponential function that decays over time, where -0.1 is the decay coefficient and \(t\) is the time. This formula calculates the risk pressure propagating upward from downstream nodes and takes into account the time decay effect.

[0157] The breadth - first search algorithm is used to update the states of affected nodes until the network state is stable, thus completing the iteration of cascading propagation. Then, a correction term is introduced to weaken the excessive influence of high - hub nodes to improve the traditional PageRank algorithm for evaluating the influence of node failures. The specific formula is expressed as:

[0158] \(PR(i)=(1 - d) / N + d\cdot\sum\) j∈M(i) [(w ij (t) / \sum k∈O(j) w jk (t))(PR(j) / CB(j) 0.5 )];

[0159] In the formula: \(d\) takes 0.85 as the damping coefficient, \(M(i)\) is the set of nodes pointing to \(i\), and \(O(j)\) is the set of out - edge nodes of \(j\). \(PR(i)\) represents the PageRank value of node \(i\) and is used to evaluate the importance of the node in the network; \((1 - d) / N\) represents the basic random walk probability, and \(N\) is the total number of nodes in the network; \(w\) ij (t) represents the weight from node \(j\) to node \(i\) at time \(t\); \(\sum_{k\in O(j)}w\) jk (t) represents the sum of the weights of all edges starting from node \(j\); \(PR(j)\) represents the PageRank value of node \(j\); \(CB(j)\) represents the betweenness centrality of node \(j\) and is used to adjust the importance transfer; \(d\) is the damping coefficient, taking the value of 0.85, which represents the probability of continuing to walk along the network. This formula calculates the importance degree of nodes in the risk propagation network by combining network structure information and node centrality.

[0160] In summary, the risk propagation at the simulation outline level is simulated, and the influence of node failures is calculated and sorted.

[0161] The time - varying SIR model is used to establish the risk propagation model at the target level. First, the state of each target - level node is quantified into a three - dimensional sub - state representation, namely the susceptible sub - state, the infected sub - state, and the recovered sub - state, which is expressed as:

[0162] Si(t) = [s i S (t), s i I (t), s i R (t)]; and it satisfies the constraint: s i S (t) + s i I (t) + s i R (t)=1 (0 ≤ s i * (t) ≤ 1);

[0163] Si(t) represents the state vector of node i at time t; s i S (t) represents the probability that node i is in the susceptible state at time t; s i I (t) represents the probability that node i is in the infected state at time t; s i R (t) represents the probability that node i is in the recovered state at time t; The constraint ensures that the sum of the probabilities of the three states is 1, and the probability value of each state is between 0 and 1.

[0164] The susceptible sub - state (S) represents the state where the node is operating normally but there is a possibility of risk exposure, and its calculation formula is:

[0165] s (S) i = (Q cap - |Q in - Q out |) / Q cap × e -λt ; where: λ = 0.05h -1 is the environmental risk accumulation rate.

[0166] The infected sub - state represents the state where risk events such as siltation, ecological deterioration, or exceeding the safe flow occur in the node, and its calculation formula is: s i I = 1 / (1 + exp(-α·(Δh / h crit +Δt fail / T resp )));

[0167] where: s i IThe probability that node i is in the infected state; α is the shape coefficient, with a value of 2.5, used to adjust the steepness of the Sigmoid function; Δh represents the deviation between the actual water head and the designed water head; h crit Represents the critical water head deviation threshold; Δt fail Represents the time after the occurrence of a fault; T resp Represents the emergency response time threshold.

[0168] The recovery sub-state represents the state where risks are eliminated by taking measures such as dredging and ecological restoration. The expression is:

[0169] s i R = tanh(β·∫ t t0 m(τ) dτ);

[0170] In the formula: m(τ) is the intensity of maintenance resource input, s i R Represents the probability that node i is in the recovered state; tanh is the hyperbolic tangent function, which maps the input to the interval (-1, 1). Here, it is used to map the degree of recovery to the interval [0, 1); β is the recovery efficiency coefficient, with a value of 0.3, representing the efficiency of converting maintenance resources into recovery effects; ∫ t0 t m(τ)dτ represents the cumulative input of maintenance resources from the start time t0 of the fault to the current time t; m(τ) represents the intensity of maintenance resource input at time τ.

[0171] Based on the initial states of each node determined through expert guidance, the following system of state transition differential equations is constructed to represent the transitions between states, expressed as: ds i S / dt = -∑ j∈N(i) w ji (t)·s j I s i S + γi(t)·s i R ; ds i I / dt =∑ j∈N(i) w ji (t)·s j I ·s i S - μi(t)·s i I ; ds i R / dt = μi(t)·si I -γi(t)·s i R ; where: N(i) represents the set of upstream adjacent nodes of node i; wji(t) represents the time-varying infection rate coefficient, which is positively correlated with the hydraulic connectivity; μi(t) represents the time-varying recovery rate, which is related to the input of maintenance resources; γi(t) represents the immunity decay rate, and generally takes a value of 0.01 h -1 。

[0172] In summary of the above steps, a time-varying SIR model at the target level is constructed to simulate the risk propagation within this level. By taking into account the time-varying factors, the transition ratio between the sub-states of each node considering the time-varying factors can reflect the influence of risks on each node better than the general single-node state.

[0173] To establish a risk propagation model at the junction level, first abstract the real-time state of the junction-level nodes into a five-dimensional vector, expressed as: V i (t) = Q in (t), Q out (t), h res (t), σ(t), τ delay (t)] T ;

[0174] where: Q in (t), 、 Q out (t) respectively represent the average inflow and outflow flow rates during a period, with the unit of m 3 / s; h res represents the deviation rate of the water level in front of the dam from the design water level, expressed as a percentage; σ represents the structural health index calculated based on the crack width, seepage flow rate, material fatigue degree, etc.; τ delay represents the emergency response delay time, with the unit of minutes. Among them, the parameters are normalized using the range method.

[0175] Based on the definition of the multi-dimensional state vector of the node and the parameter calibration, a dynamic calculation model for the weight of the directed edge is constructed. First, define the basic conduction coefficient of edge e ij for calculating the hydraulic correlation strength, and the calculation formula is:

[0176] w ij base = (Q * ij ·L ij -0.7 ) / (1 + 0.3|ΔZ ij |);

[0177] where: Q*ij is the average flow rate over the past 30 days; L ij is the length of the river or pipeline between node i and node j, in km; ΔZ ij is the elevation difference between nodes, in m.

[0178] Establish fuzzy evaluation indicators, use trapezoidal membership functions to quantify the risk levels of each indicator, and obtain the node risk entropy value through a weighted synthesis operator. Then establish a reaction-diffusion type risk propagation equation, expressed as:

[0179] dR j / dt = D j ▽ 2 R j + ∑(i∈Γ j - )α ij R i (t - τ ij ) - β i R j n ;

[0180] where: D j = 0.1L 0.5 j represents the spatial diffusion coefficient, in km 2 / h; Γ - j represents the set of upstream nodes of node j; τ ij = L ij / v ij represents the risk conduction time delay; β j = 0.03(1 - σ j ) represents the risk natural decay rate. Set the risk value of the boundary node, and the end node satisfies dR / dx = 0. Use the finite volume method to discretely solve the risk propagation equation, expressed as:

[0181] R j n+1 = R j n + Δt[D j (R j+1 n - 2R j n + R j-1 n ) / Δx 2 + S j n ; where: S n j is the source term, including upstream input and self-decay; the time step satisfies the CFL stability condition Δt ≤ Δx 2 / (2D max )。

[0182] In summary of the above steps, at the knot level, the limitation of single-index risk assessment is broken through by multi-state fusion, realizing the coupling of multiple physical fields; the directional difference of risk conduction between upstream and downstream is characterized by delay differential equations; in addition, the generalization ability of the model is improved by combining data-driven fuzzy evaluation and the diffusion equation of physical mechanism.

[0183] Based on the construction of risk propagation models at each level, a cross-level risk propagation model is constructed based on the upstream and downstream water system hydraulic connection relationships between the outline, item, and knot levels. In this embodiment, first, a cross-level dominance matrix is constructed, and the dominance matrix D = [d kl is defined. The outline-item dominance matrix D G-M is a sparse matrix, and the non-zero elements satisfy the condition:

[0184] When the annual water diversion volume of item node l ≥ 0.5Q Gk , dkl = 1, otherwise it is equal to 0.

[0185] The item-knot dominance matrix D M-J , and its elements represent the dependence degree of scheduling instructions. A cascade reaction equation set is established to express the risk propagation between cross-levels, and the expression is as follows:

[0186] dR J / dt = ∑ m∈ΓM(J) μ mJ R m (t - τ m , J ) + ∑ g∈ΓG(J) η gJ R g (t - τ gJ ) – γ J R J ;

[0187] Where: m mJ = Q mJ / Q 总 m ·e -0.1L Mj represents the propagation coefficient from the item level to the knot level; h gJ = 0.2·A g / A J represents the direct propagation coefficient from the outline level to the knot level; t gJ = max(L gm / v gm , L mJ / v mJ ) represents the calculation of time delay. The above process represents the forward mechanism from the outline level to the item level to the knot level. Next, a reverse feedback mechanism is established, and the definition is as follows:

[0188] ΔR m = ∑ j∈J(m) (dR j / dt)(S j / S m )·cosθ jm ;

[0189] Where: ΔR m represents the risk change of the target-level node m, dR j / dt represents the instantaneous risk change rate of the junction-level node j, q jm represents the topological angle between the junction node j and the target node m; S j / S m is the engineering scale ratio between the junction node and the target node.

[0190] ΔR g = ∑ m∈M(g) (dR m / dt)(S m / S g )·cosθ mg ;

[0191] Where: ΔR g represents the risk change of the outline-level node g, dR m / dt represents the instantaneous risk change rate of the target-level node m, q mg represents the topological angle between the target node m and the outline node g; S m / S g is the engineering scale ratio between the target node and the outline node.

[0192] In this embodiment, first, a complex network of each level of outline, target, and junction is established based on the water network topological structure. On this basis, a risk propagation model for each level is established according to the number of nodes at each level and the characteristics of the risk influence range, and a cross-level risk propagation model is established according to the connection relationship of the water systems between upstream and downstream. Thus, the correlation research between the water network topological structure and the risk propagation dynamics is realized, providing a systematic research idea for the research on the risk propagation law of complex water network systems and providing a research model for the research on basin risk propagation.

[0193] According to one aspect of the present application, the step S4 is further as follows:

[0194] Step S41: Perform intelligent local attacks and dynamic random attacks on the global real-time risk propagation network model to obtain the set of failed nodes at each level under the attacks, and obtain the vulnerable nodes and key risk paths at each level through vulnerability quantification and propagation path discovery;

[0195] Step S42: Based on the difference in the impact effect of risk occurrence among levels, set a level amplification factor to map the vulnerable nodes and key risk paths among levels, and identify the vulnerable levels and key risk paths of the entire water network system.

[0196] In this example, based on the complex network, risk propagation model of each level, and cross-level risk propagation model established in Step S3, analyze the vulnerable nodes and key risk paths of each level; based on the water system connection relationship and node level mapping among levels, analyze the vulnerable levels of the entire water network system and the key risk paths of the system.

[0197] Use the improved PageRank algorithm to perform intelligent local attacks on the complex networks of each level to obtain the failure node sets of each level; calculate the initial load of the nodes in the physical network layer, and based on the constructed cascade trigger simulation mechanism, perform dynamic random attacks on the complex network. At the initial attack, randomly remove the nodes whose load exceeds the threshold among the nodes, and update the load of the remaining nodes in real time after each round of attack to obtain the cascade failure node sequence and the fragmentation degree of each level after the attack ends. The fragmentation degree is represented by calculating the fragmentation coefficient. Based on the failure node sets and inter-layer coupling relationships formed after intelligent local attacks and dynamic random attacks, construct a coupled percolation model to obtain the cascade failure path, and use the Monte Carlo simulation method to statistically obtain the critical attack ratio of network connectivity mutation to obtain the percolation threshold; according to the cascade failure path and the percolation threshold, define and calculate the vulnerability index of the nodes to obtain the vulnerability ranking of the nodes, and use the improved random walk algorithm to identify the key risk propagation path; thus, obtain the vulnerable nodes and key risk propagation paths of each level.

[0198] According to the differences in the functions of the water network levels, define the amplification coefficient of risk transfer among levels, and calibrate the coefficient through expert experience; map the failure nodes of the class level to the order level through the amplification coefficient, and then the order level is mapped to the section level through the amplification coefficient, and calculate the superimposed node vulnerability scores in turn. Integrate the key risk paths of each level to construct the key risk propagation path of the water network system, and thus analyze and obtain the key risk levels of the water network system and the overall key risk path. Thus, the risk evolution laws of each level and the risk characteristics of the entire system are analyzed respectively, which is conducive to carrying out targeted risk control measures for vulnerable risk nodes and key risk paths, and maximizing the system security and comprehensive benefits to the greatest extent.

[0199] According to one aspect of the present application, the specific outputs of the present invention include:

[0200] The vulnerable nodes and key risk paths of the class, order, and section levels in the complex water network system, as well as the vulnerable levels of the complex water network system and the key risk paths of the overall system.

[0201] In this embodiment, through the above steps, the vulnerability nodes and key risk paths at each level in the complex water network system of a certain basin are obtained, and the vulnerability levels of the entire water network system and the key risk paths of the overall system are obtained, providing a new solution for identifying the risk evolution law of the complex water network system, and having high innovation and practical significance.

[0202] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the specific details in the above embodiments. Within the scope of the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention, and these equivalent transformations all belong to the protection scope of the present invention.

Claims

1. A dynamic identification method for the risk evolution law of complex water network systems, characterized in that It includes the following steps: Step S1: Collect the basic information of water conservancy projects in the water network research area and identify risk factors to obtain a risk factor sample set; Step S2: Divide the water conservancy projects in the water network research area into a hierarchical structure of three levels of outline, category, and node with mutual feedback, construct a multi-objective real-time risk scheduling model, use the risk factor sample set as input and solve it to obtain a risk scheduling plan set; Step S3: Combine the risk scheduling plan set and aim at the hierarchical structure of the complex water network system, establish a real-time scheduling risk propagation model for each level, sequentially analyze the risk propagation mechanism within each level of outline, category, and node, and establish a node domination mapping between levels according to the water system connection relationship between levels to obtain a global real-time risk propagation network model; Step S4: Based on the global real-time risk propagation network model, identify the vulnerable nodes and key risk paths at the outline, category, and node levels respectively, and perform cross-level node domination mapping on them to identify the vulnerable levels and key risk paths of the entire water network system; The further description of step S3 is as follows: Step S31: Read and establish a complex network for each level based on the hierarchical structure, generalize the water conservancy projects at each level as nodes, and establish a directed edge between nodes with direct hydraulic connections; Step S32: Analyze the differences in the number of nodes and the influence range at each level of outline, category, and node, and construct a real-time scheduling risk propagation model for each level based on the complex network of each level; Step S33: Based on the connection relationship of the water system between the upstream and downstream of the water network in the research area, construct a cross-level risk propagation mapping mechanism in which the nodes at the outline level map and dominate the nodes at the category level, and then the nodes at the category level map and dominate the nodes at the node level, and construct a global real-time risk propagation network model between levels; The further description of step S32 is as follows: Step S32a: Establish a pressure wave propagation dynamics model for simulating risk propagation for the outline level, calculate the failure influence of each node and sort them; Step S32b: Establish a time-varying SIR model for the category level, divide the state of each node into a susceptible sub-state, an infected sub-state, and a recovered sub-state, and at each moment, the sum of the weights of the sub-states of each node is 1; Step S32c: Establish an asymmetric risk diffusion model for simulating risk propagation for the node level, and the weight of the directed edge between nodes represents the risk conduction intensity.

2. The dynamic identification method for the risk evolution law of a complex water network system according to claim 1, characterized in that The further description of step S4 is as follows: Step S41: Perform intelligent local attacks and dynamic random attacks on the global real-time risk propagation network model to obtain the set of failed nodes at each level under the attack, and obtain the vulnerable nodes and key risk paths at each level through vulnerability quantification and propagation path discovery; Step S42: Based on the differences in the occurrence of risks between levels, set a level amplification coefficient to map the vulnerable nodes and key risk paths between levels, and identify the vulnerable levels and key risk paths of the entire water network system.

3. The dynamic identification method for the risk evolution law of a complex water network system according to claim 2, wherein The further description of step S41 is as follows: Step S41a: Calculate the node attack priority based on the node topological attributes and dynamic weights, give priority to attacking nodes with node topological attributes higher than the preset threshold, and generate a set of local attack failed nodes; Step S41b: Adaptively adjust the attack frequency according to the real-time network status, randomly select nodes to inject attack traffic, record the nodes whose failure ratio exceeds the critical value, and generate a dynamic attack failure node set. Step S41c: Integrate the local attack and the dynamic attack failure node set, calculate the node influence factor through the vulnerability quantification model, and combine the discovery of the propagation path to obtain the vulnerability nodes and key risk paths at each level.

4. The dynamic identification method for the risk evolution law of a complex water network system according to claim 2, wherein The step S42 is further as follows: Step S42a: Based on the hierarchical topology structure of the water network system, establish a risk transfer matrix to analyze the coupling effect between adjacent levels, and thus set the risk amplification factor of each level. Step S42b: Map the vulnerability nodes and key risk paths at each level based on the hierarchical risk amplification factor to identify the vulnerable levels and key risk paths of the entire water network system.

5. The dynamic recognition method for the risk evolution law of a complex water network system according to claim 1, characterized in that The step S1 is further as follows: Step S11: Collect the basic information of water conservancy projects in the water network research area, identify the risk factors from them, and screen out the risk factor set. Step S12: Read the risk factor set and use the spectral clustering method with balanced inter-group sizes to group the risk factor set. For each group of related and unrelated risk factors, construct the risk factor distribution, including the joint distribution of related risk factors and the distribution of unrelated risk factors. Step S13: Generate a sample set of risk factors according to the risk factor distribution, use the entropy-regularized Wasserstein optimal transport algorithm to obtain a spatio-temporally aligned mixed sample set, and test and correct it to obtain the risk factor sample set.

6. The dynamic identification method for the risk evolution law of a complex water network system according to claim 5, wherein In the step S12, the spectral clustering method with balanced inter-group sizes is specifically as follows: Based on the risk factor set, identify the related risk factors and unrelated risk factors among them. Set the group size and the number constraint of related risk factors within the group, test and adjust the risk factors of the classification clusters to obtain the grouping of the risk factor set.

7. The dynamic identification method for the risk evolution law of a complex water network system according to claim 1, characterized in that The step S2 is further as follows: Step S21: Divide the water conservancy projects in the water network research area into a three-level hierarchical structure of outline, category, and node with mutual feedback to construct a multi-objective real-time risk scheduling model. The outline level is the major water diversion and regulation projects, the category level is the river-lake connectivity projects and water transmission and distribution projects, and the node level is the water conservancy hub projects including reservoirs and pump stations. Step S22: Use the risk factor sample set as the input, map the objective functions of each level to the quantum bit superposition state, establish the inter-level correlation through the entanglement mechanism, and generate a set of risk scheduling schemes.

8. The dynamic identification method for the risk evolution law of a complex water network system according to claim 7, characterized in that In the step S21, the objective functions and constraint conditions of the multi-objective real-time risk scheduling model are specifically as follows: The outline level aims to minimize the water diversion risk, ecological impact, and economic cost. The category level aims to minimize the comprehensive risk, economic cost, and maximize the water supply benefit. The node level aims to minimize the comprehensive risk, operation cost, and maximize the comprehensive income. The constraint conditions include the water diversion capacity limit constraint and water volume balance constraint at the outline level, the project water transmission capacity limit constraint, hydraulic connection constraint, river ecological flow constraint, and water supply guarantee constraint at the category level, and the water volume balance constraint, equipment capacity constraint, hydraulic coupling constraint, and flood control control point safety constraint at the node level. Based on the objective functions and constraint conditions at each level, a multi-objective real-time risk scheduling model is constructed.

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