Dynamic identification method for risk evolution law of complex water network system

Abstract

The invention provides a complex water network system risk evolution law dynamic identification method comprising the following steps: collecting basic information and identifying risk factors to obtain a risk factor sample set; the method comprises the following steps: dividing a water conservancy project of a water network research area into a three-level mutual feedback layered structure to construct a multi-target real-time risk scheduling model, and solving to obtain a risk scheduling scheme set; establishing a real-time scheduling risk propagation model and a global real-time risk propagation network model of each hierarchy by combining the risk scheduling scheme set and aiming at the hierarchical structure of the complex water network system; and based on the global real-time risk propagation network model, respectively identifying vulnerability nodes and key risk paths of each layer, carrying out cross-level node dominating mapping on the vulnerability nodes and the key risk paths, and identifying the vulnerability levels and the key risk paths of the whole water network system. According to the method, multiple uncertainties are comprehensively considered, the calculation efficiency and the risk positioning accuracy are improved, and the method is of great significance to risk regulation and control of the water network system.

Description

Technical Field

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

[0002] Existing methods for analyzing the evolution laws of water network system risks include: Markov chain, which describes the evolution process of a random process under different states by establishing a Markov transfer matrix. The random process has the characteristic of no aftereffect, and has application limitations when dealing with problems with aftereffect; fault tree method, which decomposes the factors that constitute an accident into separate events step by step, systematically analyzes the causes of a specific event, and thus analyzes the risk transmission and evolution process, but is not widely used in large-scale modeling and analysis due to the cumbersome construction process; system dynamics theory, which analyzes and studies the feedback of information, combines qualitative and quantitative methods, explores the relationship between the system and its elements, and presents the work and behavior of the entire system through feedback loops; Bayesian network, which is essentially a probabilistic reasoning network based on Bayesian conditional probability and graph theory, which realizes the reasoning of causal relationships between variables through the marginal independence and conditional dependence probability distribution of uncertain information.

[0003] Traditional methods often rely on general classification algorithms when grouping risk factors, failing to consider the balance of scale between groups of correlated risk factors. Consequently, the actual process of constructing a joint distribution can lead to parameter explosion and inaccurate distribution construction. Furthermore, within existing research on risk scheduling and risk propagation in water networks, relatively little research has been conducted on the hierarchical structure construction and inter-layer feedback relationships within complex networks, making it difficult to accurately locate risks in complex water networks. Furthermore, the different risk targets directly determine the size of the affected area and the strength of the impact. In summary, these numerous limitations have resulted in deficiencies in existing technologies for dynamically identifying the evolution of risk patterns in complex water networks. Summary of the Invention

[0004] Purpose of the invention: To provide a method for dynamically identifying the risk evolution laws of complex water network systems to solve the above-mentioned problems existing in the prior art.

[0005] Technical solution: A dynamic identification method for the risk evolution law of complex water network systems, including the following steps: Step S1: Collect basic information of water conservancy projects in the water network study area and identify risk factors to obtain a risk factor sample set; Step S2: Divide the water conservancy projects in the water network study area into a three-level hierarchical structure of outline, project, and conclusion, and construct a multi-objective real-time risk scheduling model. Take the risk factor sample set as input and solve it to obtain a set of risk scheduling solutions; Step S3: Based on the risk scheduling scheme set and the hierarchical structure of the complex water network system, a real-time scheduling risk propagation model is established for each level. The risk propagation mechanism within the framework, item, and structure levels is analyzed in sequence. The node dominance mapping between the levels is established based on the water system connection relationship between the levels to obtain a global real-time risk propagation network model. Step S4: Based on the global real-time risk propagation network model, the vulnerability nodes and key risk paths of the hierarchy, item, and node layers are identified respectively, and cross-level node dominance mapping is performed to identify the vulnerability level and key risk paths of the entire water network system.

[0006] According to one aspect of the present application, step S3 is further: Step S31: read and establish a complex network of each layer based on the hierarchical structure, generalize the water conservancy projects of each layer into nodes, and establish directed edges between nodes with direct hydraulic connections; Step S32: Analyze the differences in the number of nodes and the scope of influence at each level of the outline, item, and knot, and construct risk propagation models at each level based on the complex network at each level; Step S33: Based on the connection relationship between the upstream and downstream water systems of the water network in the study area, a cross-level risk propagation mapping mechanism is constructed in which the framework-level nodes are mapped to dominate the item-level nodes, and then the item-level nodes are mapped to dominate the node-level nodes to construct a cross-level risk propagation network model.

[0007] According to one aspect of the present application, step S32 is further as follows: Step S32a: Establish a pressure wave propagation dynamics model for simulating risk propagation at the network level, calculate the failure influence of each node and rank them; Step S32b: Establish a time-varying SIR model for the target level, divide each node state into a susceptible sub-state, an infected sub-state, and a recovered sub-state. At each moment, the sum of the weights of each node sub-state is 1; Step S32c: Establish an asymmetric risk diffusion model for simulating risk propagation at the node level, and the weight of the directed edge between nodes represents the risk transmission intensity.

[0008] According to one aspect of the present application, step S4 is further: Step S41: Conduct 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 attack. Then, 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 risk occurrence between levels, a level amplification factor is set to map vulnerability nodes and key risk paths between levels, and identify the vulnerability levels and key risk paths of the entire water network system.

[0009] According to one aspect of the present application, step S41 is further as follows: Step S41a: Calculate the node attack priority based on the node topology attributes and dynamic weights, prioritize attacking nodes whose node topology attributes are higher than a preset threshold, and generate a local attack failure node set; 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 dynamic attack failure node sets, calculate the node impact factor through the vulnerability quantification model, and combine it with the propagation path discovery to obtain the vulnerability nodes and key risk paths at each level.

[0010] According to one aspect of the present application, step S42 is further as follows: Step S42a: Based on the hierarchical topology of the water network system, a risk transfer matrix is ​​established to analyze the coupling effect between adjacent layers, thereby setting the risk amplification factor of the layer; Step S42b: Mapping the hierarchical vulnerability nodes and key risk paths based on the hierarchical risk amplification factor to identify the vulnerability levels and key risk paths of the entire water network system.

[0011] According to one aspect of the present application, step S1 further comprises: Step S11: Collect basic information of water conservancy projects in the water network study area, identify risk factors, and screen out a risk factor set; Step S12: read the risk factor set and group the risk factor set using a spectral clustering method with balanced group size, and construct risk factor distributions for the correlated risk factors and the uncorrelated risk factors in each group, including the joint distribution of the correlated risk factors and the distribution of the uncorrelated risk factors; Step S13: Generate a sample set of risk factors according to the risk factor distribution, use the entropy regularized Wasserstein optimal transmission algorithm to obtain a mixed sample set aligned in time and space, and perform verification and correction to obtain a risk factor sample set.

[0012] According to one aspect of the present application, the step is the spectral clustering method for balancing the size between groups in S12, specifically: Based on the risk factor set, identify the correlated risk factors and non-correlated risk factors; By setting the number constraints of group size and intra-group correlation risk factors, the risk factors of the classification clusters are tested and adjusted to obtain the risk factor set grouping.

[0013] According to one aspect of the present application, step S2 further comprises: Step S21: Divide the water conservancy projects in the water network study area into a three-level hierarchical structure of outline, details, and conclusion to construct a multi-objective real-time risk scheduling model, where the outline level includes major water diversion and regulation projects, the details level includes river-lake connection projects and water transmission and distribution projects, and the conclusion level includes water conservancy hub projects such as reservoirs and pumping stations; Step S22: Taking the risk factor sample set as input, the objective function of each level is mapped into a quantum bit superposition state, and the inter-level association is established through the entanglement mechanism to generate a risk scheduling plan set.

[0014] According to one aspect of the present application, in step S21, the objective function and constraints of the multi-objective real-time risk scheduling model are specifically: The objectives of the framework level are to minimize water diversion risks, ecological impacts and economic costs; the objectives of the project level are to minimize comprehensive risks, economic costs and maximize water supply benefits; and the objectives of the structure level are to minimize comprehensive risks, operating costs and maximize comprehensive benefits. Constraints include water transfer capacity constraints and water balance constraints at the framework level; project water transfer capacity constraints, hydraulic connection constraints, river ecological flow constraints, and water supply guarantee constraints at the project level; and water balance constraints, equipment capacity constraints, hydraulic coupling constraints, and flood control point safety constraints at the node level. Based on the objective functions and constraints at each level, a multi-objective real-time risk scheduling model is constructed.

[0015] According to one aspect of this application, the specific outputs of the present invention include: The vulnerability nodes and key risk paths at the framework, item and node levels in the complex water network system, as well as the vulnerability levels of the complex water network system and the main risk transmission paths of the system as a whole.

[0016] Beneficial effect: the spectral clustering method for balancing the scale between groups proposed in the present invention takes into account both the balance of scale between groups and the correlation of factors within groups, and solves the offset problem of traditional clustering algorithms in risk factor grouping. In order to solve the complexity of solving multi-objective optimization problems, a dynamic fractal collaborative quantum optimization algorithm is proposed, which uses quantum teleportation for command transmission between levels, achieves millisecond-level cross-layer response, and reduces the complexity of the algorithm by compressing the solution space through fractal dimensions, which is suitable for the solution needs of larger-scale water network systems. In view of the differences in the scale, characteristics and risk impacts of water conservancy projects in complex water network systems, a hierarchical-specific risk propagation model is established, which realizes the study of the evolution law of risk propagation in the layering of complex water network systems. At the same time, it provides an effective reference for accurately locating risk levels, main paths of risk propagation, and core control points and paths within the levels, and has high technical innovation and practical significance. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 Flowchart of the present invention.

[0018] Figure 2 This is a flow chart of step S1 of the present invention.

[0019] Figure 3 This is a flow chart of step S3 of the present invention. DETAILED DESCRIPTION

[0020] The following is an example of a complex water network system in a certain river basin, and the technical solution of the present invention is described in detail with reference to the accompanying drawings.

[0021] like Figures 1 to 3 As 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, characterized in that it includes the following steps: Step S1: Collect basic information on water conservancy projects in the water network study area and identify risk factors. Use a multimodal dynamic weight fusion correction ranking method to comprehensively rank the risk factors based on their impact effects, screen out a risk factor set, group the risk factor set using a spectral clustering method that balances group sizes, construct distributions for the grouped risk factors, and finally construct a risk factor sample set using a coupled optimization method of stratified mixed sampling. Step S2: Divide the water conservancy projects in the water network study area into a three-level, mutually-feedback hierarchical structure of outline, project, and conclusion. Based on the principles of each level, establish the objective functions and constraints of each level, construct a multi-objective real-time risk scheduling model, use the risk factor set as input, and solve it using a dynamic fractal collaborative quantum optimization algorithm to obtain a set of risk scheduling solutions for the complex water network system; Step S3: Based on the risk scheduling scheme set and the hierarchical structure of the complex water network system, a real-time scheduling risk propagation model is established for each level. The risk propagation mechanism within the framework, item, and structure levels is analyzed in sequence. The node dominance mapping between the levels is established based on the water system connection relationship between the levels to obtain a global real-time risk propagation network model. Step S4: Based on the global real-time risk propagation network model, the vulnerability nodes and key risk paths of the hierarchy, item, and node layers are identified respectively, and cross-level node dominance mapping is performed to identify the vulnerability level and key risk paths of the entire water network system.

[0022] Traditional research on water network risk patterns generally considers only the impact of a single or a few uncertain factors, with limited consideration of comprehensive risk factors. Consequently, there is a lack of research references to address issues such as the curse of dimensionality and high computational complexity that may arise when constructing the distribution of multiple risk factors. Furthermore, complex systems typically involve a wide range of large-scale entities with diverse characteristics, making comprehensive analysis of their risk evolution patterns difficult in terms of organization and computation. Furthermore, analysis of risk characteristics lacks a clear hierarchy of priorities, hindering targeted risk management and control in production practices.

[0023] The present invention comprehensively considers the many uncertainties involved in the complex water network system, and at the same time screens risk factors with higher ranking priorities to avoid unimportant factors affecting the analysis effect. Considering the impact of a large number of risk factors on the calculation speed and efficiency, after screening out the correlated factors and non-correlated factors, a spectral clustering method with balanced inter-group scale is proposed to group the risk factor set, taking into account the balance of inter-group scale and the correlation of factors within the group, and solving the offset problem of traditional clustering algorithms in risk factor grouping. In the sampling stage based on the distribution of risk factors, a coupled optimization method of stratified mixed sampling is proposed, which takes into account the joint distribution of correlated risk factors and the independent distribution of non-correlated risk factors, and at the same time considers the influence of temporal and spatial factors to couple the two, ensuring sampling accuracy and efficiency.

[0024] The complex water network system is huge, and the water conservancy projects in the water network study area have complex hydraulic connections, which makes it difficult to directly construct a real-time risk scheduling model. In the present invention, the water network system is considered to be divided into a three-level hierarchical structure of "outline, heading, and knot" according to the scale and characteristics of the water conservancy projects. The water conservancy projects within and between 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 goals during operation. In the research of the present invention, the objective function of the level is established by comprehensively considering the criteria of each level, and a multi-objective optimization problem is established for collaborative optimization of the three-level objective functions. At the same time, in order to solve the complexity of solving the multi-objective optimization problem, a dynamic fractal collaborative quantum optimization algorithm is proposed, and quantum teleportation is used for instruction transmission between levels, achieving millisecond-level cross-layer response, and reducing the algorithm complexity by compressing the solution space through fractal dimensions, which is suitable for the solution needs of larger-scale water network systems. In addition, the established dynamic equilibrium entropy mechanism combines quantum annealing with classical entropy indicators to solve the stability problem in multi-objective solution set screening.

[0025] In studying risk propagation patterns, complex network theory was applied to construct hierarchical complex networks, achieving a graphical integration of water network topology and risk propagation analysis, laying the foundation for risk propagation analysis. Taking into account the differences in the number of nodes at different levels and the range of risk impact within the water network, targeted risk propagation models were developed at each level to simulate risk evolution within that level. Furthermore, based on the connectivity between upstream and downstream water systems, an inter-level risk propagation mechanism was established. This provides a new research method and paradigm for analyzing risk propagation patterns in complex water networks.

[0026] 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, and the vulnerability nodes and key risk paths at each level are identified. Based on the differences in the impact effects between risk levels, the amplification coefficients of the levels are set to perform risk mapping between levels, and the vulnerability levels and key risk paths of the entire system are obtained, which is conducive to the targeted risk regulation of the water network system.

[0027] According to one aspect of the present application, step S1 further comprises: Step S11: Collect basic information on water conservancy projects in the water network study area, and use a brainstorming-literature mining-reduction-Delphi synthesis method to identify risk factors; organize and preprocess the risk factor data to obtain a multimodal data set and calculate the multimodal fusion eigenvalues ​​of the risk factors; sort the risk factors based on the multimodal fusion eigenvalues, use an exponential spatiotemporal decay kernel function to correct the sorting, and apply the Pareto analysis method to select the sorted risk factors to obtain a risk factor set; In this embodiment, the required basic information can be collected from public data. The basic information of water conservancy projects mainly includes hydrological, geological and engineering operation data. The data types include numerical data, text data and spatiotemporal data, so as to achieve the purpose of in-depth understanding of the basic situation and hydrological characteristics of the water network study area, and provide basic information and data support for subsequent model design and construction.

[0028] According to one aspect of the present application, in step S11, the specific steps of calculating the multimodal fusion feature value of the risk factor are: The risk factor data are organized according to numerical, textual, and spatiotemporal types. The organized data are preprocessed separately: the numerical data are normalized, the textual data are word segmented and vectorized, and the spatiotemporal data are rasterized, spatially interpolated, and time-aligned. This results in a multimodal dataset of risk factors in numerical, textual, and spatiotemporal modes. Based on the pre-processed multimodal risk factor dataset, we extract modal features separately. For numerical modalities, we use the time series feature extractor Transformer to extract trend, cycle, and outlier features. For textual modalities, we use the pre-trained language model BERT to extract semantic features. For spatiotemporal modalities, we use the spatiotemporal Transformer to extract spatial dependency and temporal evolution features. Based on expert experience, the initial weights of numerical, textual, and spatiotemporal modalities are set, and the Choquet fuzzy integral is used to fuse multimodal features. The game model is applied to dynamically update the weights of each modality based on the strategy of adjusting its own weight to maximize the rationality of the overall ranking. The gradient descent method is used to iteratively optimize the modal weights to obtain the multimodal fusion feature value of the risk factor.

[0029] In this embodiment, the risk factors identified by the brainstorming-literature mining-reduction-round Delphi synthesis method are extensive, so the risk factors are screened by using a multimodal dynamic weight fusion correction ranking method.

[0030] First, 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. 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 are normalized, the text data are word segmented and vectorized, and the spatiotemporal data are 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 separately, 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 Contained 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 (arranged 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 the weight to maximize the rationality of the overall ranking. The three modes of value, text and time and space are used as "players". The profit function is defined based on the Kendall Tau correlation coefficient τ, and the expression formula is: Revenue 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. Its formula is: ω i t+1 =ω i t +η·dConsistency / dω i , where η represents the learning rate, which is used to control the weight adjustment speed; Revenue i represents the revenue value of the i-th modality; τ represents the ranking consistency metric; model ranking refers to the ranking result generated by the algorithm; expert ranking refers to the manually labeled ranking result; ω i is the current modality 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 is the partial derivative.

[0031] Thus, the multi-modal fusion eigenvalue of the risk factor is obtained, and the risk factors are sorted in descending order according to the multi-modal fusion eigenvalue; finally, the exponential spatio-temporal decay kernel function is used to lower the ranks of the risk factors that are long ago in history and far away in space, and the Pareto analysis method is used to select the top 80% of the sorted risk factors as the risk factor set.

[0032] In this embodiment, first, multi-modal learning in computer vision and natural language processing is used to jointly represent multi-source information to enhance the complementarity between information and expand the utilization of the water network information in the study area; then, the fuzzy integral method is used to enhance the processing of non-additive weights and achieve the fusion of multi-modal data; the numerical, text, and spatio-temporal modalities are regarded as game participants respectively, and the ranking of risk factors is obtained by optimizing the weight allocation strategy through the Nash equilibrium; finally, the ranking result is optimized and the top 80% are selected to form the risk factor set. Thus, compared with the disadvantages of traditional fixed weights and isolated processing of multi-modal data, the multi-modal dynamic weight fusion correction ranking method that combines fuzzy integral, game model, and expert evaluation feedback embedded in the game revenue function achieves the effect of real-time response to data changes and cross-modal collaboration.

[0033] Step S12: Read the risk factor set, identify the associated risk factors and non-associated risk factors, group the risk factor set using the spectral clustering method that balances the group sizes, construct the joint distribution of the associated risk factors using the adaptive unit joint distribution, select the distribution type using the Bayesian information criterion and perform the goodness-of-fit test to obtain the distribution of the non-associated risk factors; A large number of risk factors were screened in the water network study area. Directly establishing a joint distribution for the associated risk factors presents problems such as the curse of dimensionality, high computational complexity, and error accumulation. To address this issue, this embodiment proposes a spectral clustering method that balances the scale between groups to group the risk factor set, thereby achieving the goal of controlling the scale of the associated risk factors within each group.

[0034] According to one aspect of the present application, step S12 is further as follows: Step S12a: construct a hypergraph model based on the risk factors, using the risk factors as hypergraph nodes and constructing initial state hyperedges based on the node information. Define a cross-entropy loss function and apply the gradient descent method to update the hyperedge weights through back-propagation optimization. Filter risk factor nodes whose hyperedge weights exceed a threshold as risk factors with relevance, where the threshold is determined by the cross-entropy loss. Step S12b: Based on the identified sets of associated risk factors and non-associated risk factors, conditional mutual information is calculated and a permutation test is performed to generate a sparse association matrix; a normalized Laplace matrix is ​​constructed based on the association matrix, and eigenvector mapping is solved by semidefinite programming to generate a low-dimensional embedding space and a dispersed distribution of strong association factors in the embedding space; a capacity-sensitive greedy algorithm is used in the embedding space to obtain grouping of risk subsets; Step S12c: construct a multidimensional joint distribution space based on the associated risk factors, use a density-based spatial clustering method for initial partitioning, optimize the distribution unit boundaries in combination with the information entropy constraint criterion, test the homogeneity of the data within the unit through KL divergence, use kernel density estimation to construct the local probability density function of each unit, and finally use the Copula function to fuse the marginal distribution and the dependency structure to establish a non-parametric joint distribution; Step S12d: Preliminarily screen candidate distributions based on the data characteristics of non-correlated risk factors, use the EM algorithm to gradually fit the candidate distributions and estimate parameters, select the optimal distribution type based on the Bayesian Information Criterion, and use the KS test to perform a goodness of fit test to obtain the distribution and parameters of non-correlated risk factors.

[0035] In this embodiment, a hypergraph model is first constructed to divide the risk factor set into a correlated risk factor set and an uncorrelated risk factor set. The risk factors within the group are used as hypergraph nodes, and the initial state hyperedges are constructed with the risk factor information. The cross entropy loss function formula is defined as follows: L =-∑ e∈E [p true (e)·log(p model (e))+(1-p true (e))·log(1-p model (e))].

[0036] Wherein, L represents the sum of all hyperedge cross-entropy losses, i.e., the total loss; p true ( e ) represents the frequency of occurrence of hyperedge e in historical events (normalized to probability), p model ( e ) = σ(ω e ) represents the hyperedge weight ω e The probability after mapping through the Sigmoid function; after defining the cross-entropy loss function, the hyperedge weight is updated by backpropagation through the gradient descent method, which improves the model's ability to express complex association patterns. The gradient descent method formula 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 hyperedge weight; finally, a threshold dynamically adjusted by the cross-entropy loss function is set to screen the risk factor nodes with hyperedge weights exceeding the threshold, and determine them as risk factors with significant relevance. This process avoids manual setting bias through the adaptive threshold mechanism and ensures the statistical significance of the screening results.

[0037] 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 test (set the threshold λ = 0.3 in this embodiment), generate a sparse association matrix A, only retain the significant association 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 for balanced spectral clustering: min Y {Tr(Y T L m Y)}, s.t. Y T ·Y = I k , for any i, ||Y i ||0 ≤ s max . Wherein,Y ∈ R n×k represents the cluster indicator matrix, I k represents the identity matrix, s max Indicates the maximum capacity of a single group (s max =⌈n / k⌉+δ, δ is the tolerance threshold), and then the semidefinite programming is used to solve the constrained eigenvalue problem and extract the previous k The eigenvectors map the original data into a low-dimensional embedding space. In this space, strong correlation factors are naturally dispersed thanks to the orthogonality constraints of the Laplace matrix, avoiding the problem of dimensionality curse caused by excessive concentration of correlation risk factors in a certain group. Finally, the weighted k-means algorithm is used to initialize the cluster centers in the low-dimensional embedding space to ensure a balanced geographical distribution of the initial groups. For groups that exceed the capacity limit, the correlation overlap with the adjacent groups is calculated: ρ=∑ i∈Gp,j∈Gq A ij / sqrt(|Gp||Gq|), where ρ represents the degree of association overlap, Gp represents the currently processed group, and Gq represents the adjacent group being compared with Gp. When ρ > 0.7, highly overlapping groups are merged, and then a capacity-sensitive greedy algorithm is used to redistribute excess factors to the weakest adjacent groups, ultimately keeping the size difference between groups within 20%. This method achieves a balance between intra-group association strength and grouping uniformity, providing optimal input for subsequent joint probability distribution modeling.

[0038] For correlated risk factors, density-based spatial clustering was used to initially partition the multidimensional data. Information entropy constraints were then applied to optimize the boundaries of distribution units to ensure data homogeneity within the units (verified by the KL divergence test). Kernel density estimation was used to construct local probability density functions for each distribution unit. Copula functions were then used to integrate the marginal distributions and dependency structures of each unit, ultimately establishing a nonparametric multidimensional joint distribution model. This approach avoids the strong assumptions about data morphology made by traditional parameterized distributions and improves the model's generalization capabilities. For uncorrelated risk factors, candidate distributions were initially screened based on data characteristics such as skewness and kurtosis, including the normal distribution, Weibull distribution, and generalized Pareto distribution. The EM algorithm was used to progressively fit distribution parameters. The optimal type was selected from the candidate distributions based on the Bayesian Information Criterion. The KS test was used to verify the goodness of fit, ultimately determining the distribution type and parameters for the uncorrelated risk factors.

[0039] In summary, in this embodiment, by balancing the spectral clustering and hypergraph model of the inter-group scale, the balance of the inter-group scale and the correlation of the factors within the group are taken into account, and the offset problem of the traditional clustering algorithm in the risk factor grouping is solved. By combining the cross entropy loss function with the gradient descent method, the dynamic adjustment of the correlation factor screening threshold is realized, and the problem of possible overfitting of the model caused by manual intervention is reduced. Finally, by fusing the non-parametric kernel density estimation and the Copula function, the nonlinear dependency structure of complex risk factors can be effectively characterized, and the robustness of the joint distribution establishment of the correlation risk factors is improved. In short, through multi-stage optimization and statistical testing, this embodiment achieves efficient modeling of high-dimensional risk factors and accurate risk quantification.

[0040] Step S13: Generate a sample set of risk factors according to the risk factor distribution, use the entropy regularized Wasserstein optimal transmission algorithm to obtain a mixed sample set aligned in time and space, and perform verification and correction to obtain a risk factor sample set; According to one aspect of the present application, step S13 is further as follows: Step S13a: Based on the joint distribution of the correlation risk factors, a sample set of correlation risk factors is obtained using a reversible neural network and Hamiltonian Monte Carlo hybrid method; Step S13b: Based on the distribution and parameters of the non-correlated risk factors, a sample set of non-correlated risk factors is obtained by using quantum state discretization and Grover search acceleration method; Step S13c: Based on the sample set of correlated risk factors and the sample set of uncorrelated risk factors, the entropy regularized Wasserstein optimal transmission algorithm is used to process the temporal and spatial distribution differences between the sample sets to obtain a temporally and spatially aligned mixed sample set; Step S13d: Calculate statistical indicators such as KL divergence, HSIC dependence intensity, and extreme event coverage to test the mixed samples, use online feedback control and local resampling mechanism to correct errors, and obtain a risk factor sample set.

[0041] In this embodiment, the problem of sampling complex risk factors across time, space, and multiple dimensions is solved by innovatively integrating a classical-quantum hybrid algorithm with a dynamic optimization mechanism. For correlated risk factors, a reversible neural network and Hamiltonian Monte Carlo hybrid method are used to achieve precise sampling in high-dimensional nonlinear joint distributions, balancing the integrity of distribution characteristics with computational efficiency. For uncorrelated factors, quantum state discretization and a Grover search acceleration algorithm are used to overcome the efficiency bottleneck of classical discretization to a certain extent, reducing the sampling complexity of large-scale sparse distributions. Based on the entropy-regularized Wasserstein optimal transmission algorithm, differences in the temporal and spatial distributions of samples are intelligently eliminated, maintaining the temporal and spatial coupling characteristics of risk factors. A quality assessment system is constructed through multi-dimensional statistical tests such as KL divergence and HSIC. Key indicators such as extreme event coverage are dynamically corrected using online feedback control and a local resampling mechanism to ensure that the sample set achieves the optimal balance between statistical significance and risk coverage completeness. Overall, this step provides a high-fidelity and efficient sampling modeling method, improving the accuracy of quantitative analysis of complex risk systems.

[0042] According to one aspect of the present application, step S2 further comprises: Step S21: Divide the water conservancy projects in the water network study area into a three-level hierarchical structure of outline, details, and conclusion to construct a multi-objective real-time risk scheduling model, where the outline level includes major water diversion and regulation projects, the details level includes river-lake connection projects and water transmission and distribution projects, and the conclusion level includes water conservancy hub projects such as reservoirs and pumping stations; In this example, the complex water network system in a certain river basin is large, and the hydraulic connections between the water conservancy projects in the water network study area are complex, making the construction of a real-time risk scheduling model quite difficult. Therefore, a three-level hierarchical structure is proposed, based on the attributes and scale of the water conservancy projects in the water network study area: outline, item, and node. The outline-level water conservancy projects include a certain river section and the X-to-X-River Diversion Project. The item-level water conservancy projects include the X-to-X main canal system, the X-to-X-River main stream-X ecological water replenishment channel, and the AB water transfer channel. The node-level water conservancy projects include the X-to-X reservoir, the X-to-X reservoir, as well as the X-to-X sluice pump station group and the X-to-X flood control project.

[0043] Based on the three-level division of the water network study area and incorporating the principle of fractal self-similarity and the hydraulic connections between upstream and downstream water conservancy projects, the water network system is decoupled into three decision-making dimensions: the fractal primary dimension at the framework level serves as the macro-level topology optimization layer, the fractal secondary dimension at the item level serves as the meso-level path planning layer, and the fractal primitive dimension at the node level serves as the micro-level node regulation layer. A dynamic feedback mechanism is established between the layers, consisting of a forward command flow, a reverse information flow, and a horizontal coordination mechanism. The forward command flow represents the transmission of information from the framework level to the item level, ultimately reaching the node level for response. The reverse information flow represents the process of information transmission from the node level, through the item level, and then back to the framework level. The horizontal coordination mechanism is a process of information transmission from the item level to the framework level and then to the node level, with the item level as the transmission core. This results in a complex water network system with dynamic multi-level feedback loops. On the one hand, the hierarchical division makes the structural hierarchy of the complex water network system clear, the risk impact effects and scope within the same level are similar, and there are obvious differences between the levels, which facilitates the accurate positioning of risk analysis; on the other hand, the levels are connected through the upstream and downstream hydraulic connections inherent in the water network system, which is different from the connection between levels in general complex systems. This makes the three levels have both research independence and close connections, and does not form isolated levels. It is of great significance to the study of complex water network systems.

[0044] According to one aspect of the present application, in step S21, the multi-objective real-time risk scheduling model is specifically: Framework level: The goal is to minimize water diversion risks, ecological impacts, and economic costs, expressed as: F 纲 =g1 R 调水 +g2 R 生态 +g3 C 经济 ; Among them, R 调水 =∑ n i=1 g i r i ; R 调水 represents the water diversion risk, and the weight is determined by the entropy weight method; R 生态 is the quantified value of ecological impact, C 经济 is the investment and operation and maintenance cost of the water diversion project, g1, g2, and g3 are the weights assigned by experts, satisfying g1+g2+g3=1; The constraints at the framework level include water transfer capacity constraints and water balance constraints, which can be expressed as: Water transfer capacity constraint: ∑ n i=1 Q调,i ≤Qmax; Where Q max Indicates the maximum water transfer capacity of the system; Water balance constraint: ∑Q 入 -∑Q 出 =ΔS; Where, Q 入 For input or transfer of water, Q 出 is the outflow or transfer water volume, Δ S Indicates the change in regional water volume; Project level: The goal is to minimize comprehensive risks, economic costs and maximize water supply benefits. Comprehensive risks mainly include flood control risks, interruption risks, ecological risks and water supply risks, which can be expressed as: 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); B water supply = ∑ m k=1 q k p k (Water supply efficiency, q k is the water supply, p k is the unit price of water supply); m1, m2, and m3 are weights assigned by experts, satisfying m1+m2+m3=1; The constraints at the project level include the project water delivery capacity constraint, hydraulic connection constraint, river ecological flow constraint, and water supply guarantee constraint, which can be expressed as: Project water delivery capacity constraints: Q k (t)≤Q cap,k , any k ∈engineeringnode; Hydraulic connection constraints: H i (t)= f ( Q i (t)), any i ∈River node; River ecological flow constraints: Q 生态,j (t)≧ Qmin,j , any j ∈Ecologically sensitive section; Water supply guarantee constraints:∑ m k=1 q k （t） ≥D 需，t ; Conclusion level: The goal is to minimize comprehensive risks, operating costs and maximize comprehensive benefits. Comprehensive risks mainly include flood control risks, water supply shortage risks, structural safety risks, ecological risks and power generation shortage risks. Comprehensive benefits mainly include power generation benefits, water supply benefits and ecological benefits, which can be expressed as: F 结 =j1 R’ 综合 +j2 C 运行 -j3 B 综合 ; in, R’ 综合 =∑ 5 l=1 w l ' r l ' (flood control risk r1', water supply insufficiency risk r2', structural safety risk r3', ecological risk r4', power generation insufficiency risk r5'); B 综合 = B 发电 + B 供水 + B 生态 (Power generation income is calculated based on electricity price and power generation, and ecological benefits are quantified based on restoration effects); j1, j2, and j3 are weights assigned by expert scoring, satisfying j1+j2+j3=1; The constraints at the node level include water balance constraints, equipment capacity constraints, hydraulic coupling constraints, and flood control point safety constraints, which can be expressed as: Device capability constraints: P 发电,i (t)≤P rated,i , any i ∈Hydropower station; Flood control point safety constraints: H 防洪,j (t)≤H 安全,j , any j ∈Flood control point; Hydraulic coupling constraints: Q 上游 ( t )= Q 下游 (t )+Δ Q 分流 ( t ); Based on the objective functions and constraints at the framework, item and node levels, a multi-objective real-time risk scheduling model for complex water network systems is constructed.

[0045] Step S22: Using the risk factor sample set as input, the objective functions of each level are mapped into quantum bit superposition states, and the inter-level associations are established through the entanglement mechanism to generate a risk scheduling solution set; According to one aspect of the present application, step S22 is further as follows: Step S22a: Map the objective functions of the hierarchy, order, and knot layers into quantum bit superposition states, where the objective functions of the hierarchy, order, and knot layers are encoded as high-order, medium-order, and low-order quantum bits, respectively; achieve three-level quantum bit entanglement through quantum gate operations to form an overall state to achieve correlation between the layers. Changes in the state of any layer will affect the states of other layers through the defined entanglement mechanism; Step S22b: Compress the solution spaces at the class, order, and knot levels into a single space through the correlation of entangled states. Use an improved quantum particle swarm optimization algorithm to adjust the particle positions in the solution space. Filter and retain elite solutions using non-dominated sorting and crowding calculation to obtain a set of risk scheduling solutions for the complex water network system. Traditional multi-objective optimization algorithms suffer from low computational efficiency. Classic algorithms such as NSGA-II and MOPSO require traversing a vast solution space. Due to the large scale of water networks, computational time increases exponentially with network size, making it difficult to meet the needs of water network risk scheduling research. Furthermore, the established multi-level, dynamically inter-feedback multi-objective risk scheduling model may have multiple local optimal solutions, and general multi-objective optimization algorithms are prone to local optimality. Furthermore, traditional algorithms are mostly static optimizations, lacking dynamic information transfer mechanisms between levels. Therefore, this study proposes a quantum particle swarm optimization algorithm that integrates dynamic fractal collaboration. Through parallel computing, quantum superposition, and entanglement, it achieves better global search capabilities and faster convergence efficiency.

[0046] In this embodiment, the specific implementation steps are as follows: first, quantum encoding is performed to map the objective functions of the hierarchy, target, and knot levels into quantum bit superposition states, with the hierarchy level objective encoded as high-order quantum bits, the target level objective encoded as mid-order quantum bits, and the knot level objective encoded as low-order quantum bits; then, fractal dimension adaptation is performed, specifically, by recursively decomposing the global optimization problem into subproblems through the self-similarity of fractal geometry, with each subproblem corresponding to a sequence of quantum gate operations; The dynamic mutual feedback transmission mechanism between the layers is realized through the quantum teleportation channel. Specifically, the network layer transmits the probability distribution of the optimal solution to the target layer through quantum teleportation technology to send optimization instructions, which avoids the delay problem of traditional communication to a certain extent. The real-time state of the node layer is fed back to the target layer through quantum measurement, triggering the dynamic adjustment of the target layer parameters. The expression is: β new = βe -γ‖ΔQnode‖ Where, β is the original weight coefficient of the target level, β new is the adjusted weight coefficient, Δ Q node is the node flow deviation, and γ is the attenuation coefficient.

[0047] In the process of quantum particle swarm co-evolution, each particle represents a solution of a fractal hierarchical combination, and its position is described by the quantum state, expressed as: |ψ>=α|0>+β|1>; Then the following update rule is used to integrate the quantum revolving door and the classical PSO speed update, expressed as: id t+1 =w·v id t +c1·R(θ pbest )+c2·R(θ gbest ); Where, R (θ) is a quantum rotating gate operation, which is used to adjust the phase of the quantum state to approach the Pareto frontier. Using the quantum annealing filter, the Pareto solution set is input into the quantum annealing machine, and the objective function is to minimize the system entropy. This screens out a set of risk scheduling solutions that take into account both stability and efficiency, which can be expressed as: S opt =argmin Si {(-∑pi ln(pi))+λ Risk Index}; where p i For the plan S i The probability of traffic distribution. Index Represents the risk indicator. id t represents the velocity of the i-th particle in the t-th iteration in the d-th dimension; v id t+1 represents the updated speed; w represents the inertia weight; c1 and c2 represent the learning factor; θ pbest represents the rotation angle corresponding to the optimal position of the individual; θ gbest represents the rotation angle corresponding to the global optimal position; S optrepresents the optimal solution set. λ is the balance coefficient.

[0048] In summary, in this embodiment, a quantum-classical hybrid architecture is constructed, and quantum teleportation is used for inter-layer instruction transmission, achieving millisecond-level cross-layer response, which is a certain improvement in timeliness compared to the traditional NSGA-II method. The fractal-quantum coupling modeling method of fractal dimension compression solution space reduces the algorithm complexity from O (n 3 ) down to O (nlogn), which is suitable for large-scale water network systems. In addition, the established dynamic equilibrium entropy mechanism combines quantum annealing with the classical entropy index to solve the stability problem in multi-objective solution set screening.

[0049] According to one aspect of the present application, step S31 is further as follows: Step S31: read and establish a complex network of each layer based on the hierarchical structure, generalize the water conservancy projects of each layer into nodes, and establish directed edges between nodes with direct hydraulic connections; Step S32: Analyze the differences in the number of nodes and the scope of influence at each level of the outline, item, and knot, and construct risk propagation models at each level based on the complex network at each level; Step S33: Based on the connection relationship between the upstream and downstream water systems of the water network in the study area, a cross-level risk propagation mapping mechanism is constructed in which the framework-level nodes are mapped to dominate the item-level nodes, and then the item-level nodes are mapped to dominate the node-level nodes to construct a cross-level risk propagation network model.

[0050] In this embodiment, a complex network of the outline, item, and node levels is first constructed, with the water conservancy projects within each level being nodes. Directed edges are established between nodes with direct hydraulic connections, realizing the combination of complex network theory and water conservancy topology, laying the foundation for the establishment of a risk propagation model for the water network system and the analysis of risk propagation characteristics. Based on the distinctive characteristics of the complex network constructed at each level of the water network, the outline level has a small number of nodes but the scope of influence of node risks in the water network is relatively wide, the node level has a large number of nodes but the scope of influence of its node risks in the water network is significantly smaller, and the item level has a relatively intermediate combination of the above two characteristics. Based on these characteristics, risk propagation models for each level are established separately. In addition, considering the correlation of risks at each level, the cross-level risk propagation mechanism is analyzed and a cross-level risk propagation model is established.

[0051] According to one aspect of the present application, step S32 is further as follows: Step S32a: Based on the fact that the number of nodes at the hierarchy level is small but the nodes have a wide influence range, a pressure wave propagation dynamics model is established to simulate the hierarchy-level risk propagation, and a node pressure deviation threshold is set. The failure influence of each node is calculated and ranked using the cascading failure propagation algorithm and the improved PageRank algorithm. Step S32b: Establish a time-varying SIR model for the target level, divide each node state into a susceptible sub-state, an infected sub-state, and a recovered sub-state. At each moment, the sum of the weights of each node sub-state is 1; Step S32c, generalize the nodes of the constructed node-level complex network into multi-dimensional state vectors, and define the directed edge weights between nodes to represent the risk transmission 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 node-level nodes.

[0052] In this embodiment, based on the construction of complex networks at the outline, item, and node levels, risk propagation dynamics models are established to simulate the risk propagation within and between levels, providing an effective reference for identifying the risk evolution laws of the water network system.

[0053] Based on the characteristics that the number of nodes at the level of the hierarchy is relatively small but the risk of each node is likely to have a greater impact within the scope of the water network study area, a pressure wave propagation dynamics model is established to simulate the spread of risk at the level of the hierarchy. Based on the nodes and directed edges of the complex network constructed at the level of the hierarchy, a weighted adjacency matrix is ​​constructed. W ( t ), where the elements w ij ( t ) represents a node i arrive j The risk transmission intensity is expressed as: w ij (t) = Q ij (t) / Q design × e -λL ij / v(t) × (1+0.2 C B ( j )); Where: Q ij (t) / Q design Indicates the traffic 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 is taken as 0.15s -1 represents the empirical attenuation coefficient, C B ( j )for j The betweenness centrality of a node reflects the degree of its hubness in the network and is normalized to [0,1]. The water hammer effect control equation is established, and the characteristic line method is used to solve the transient flow equation, which is expressed as follows: dH / dt + (c 2 / gA)·dQ / dx = 0; dQ / dt + gA·dH / dx + f Q|Q| / (2DA) = 0; in: H ( x , t ) represents the pressure tube head; c=(K / ρ) 0.5 / (1+(K / E)(D / e)) 0.5 is the water hammer wave velocity, 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 pipe wall thickness; f is the Darcy-Weisbach friction coefficient. Construct the risk pressure fluctuation equation and define the node risk pressure fluctuation P i ( t ), which is expressed as follows: Pi(t) = α·|(Hi(t)-H design ) / (H fail -H design )| + β·(dQi / dt) / Q max ; 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 Indicates the design head; H fail represents the damage head (the critical head value at which the pipeline may be damaged); dQi / dt represents the rate of change of flow at node i; Q max represents the maximum flow rate; α and β are weight coefficients, representing the contribution of head deviation and flow rate change rate to risk assessment, respectively. α = 0.7 and β = 0.3 are weight coefficients.

[0054] Establish a cascading failure propagation mechanism. First, set the node failure trigger conditions. If any of the conditions are met, the node i Will trigger an invalidation, as shown below: Condition 1: P i (t)>1.2 P threshold ; Condition 2: Existence j ∈U( i ), dP j / dt >0.5s -1 and C B ( i )>0.8; Where, U ( i ) is a node i The set of upstream nodes.

[0055] Real-time monitoring of each node P i (t), when any failure condition is triggered, it will be marked as a failure state and the pressure redistribution calculation will be performed, which is expressed as follows: ΔP prop = ∑ j∈Di w ji(t) (P j (t)-P threshold ) / (1+e -0.1t ); where D(i) is the set of nodes directly downstream of node i. ΔPprop represents the risk pressure propagation; j∈Di represents the set of nodes directly downstream 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 Indicates the pressure threshold; e -0.1t Represents an exponential function that decays over time, where -0.1 is the decay coefficient and t is time. This formula calculates the risk pressure propagating upward from downstream nodes, taking into account the time decay effect.

[0056] The breadth-first search algorithm is used to update the status of the affected nodes until the network state is stable, thus completing the iteration of cascade propagation. Then, a correction term is introduced to weaken the excessive influence of high-hub nodes to improve the traditional PageRank algorithm to evaluate the influence of node failure. The specific formula is expressed as: PR(i) = (1-d) / N + d·∑ j∈M(i) [(w ij (t) / ∑ k∈O(j) w jk (t)) (PR(j) / CB(j) 0.5 )]; Where: d is taken as 0.85 as the damping coefficient, M(i) is the set of nodes pointing to i, and O(j) is the set of nodes outgoing from j. PR(i) represents the PageRank value of node i, which is used to evaluate the importance of the node in the network; (1-d) / N represents the basic random walk probability, N is the total number of nodes in the network; wij (t) represents the weight from node j to node i at time t; ∑[k∈O(j)]w jk (t) represents the sum of the weights of all edges originating from node j; PR(j) represents the PageRank value of node j; CB(j) represents the betweenness centrality of node j, which is used to adjust the importance transfer; d is the damping coefficient, which is set to 0.85 and represents the probability of continuing to move along the network. This formula combines network structure information and node centrality to calculate the importance of a node in the risk propagation network.

[0057] In summary, the risk propagation at the hierarchy level is simulated and the impact of node failure is calculated and ranked.

[0058] The time-varying SIR model is used to establish a target-level risk propagation model. First, the state of each target-level node is quantified into three-dimensional sub-state representations, namely susceptible sub-state, infected sub-state and recovered sub-state, which are expressed as: Si(t) = [s i S (t), s i I (t), s i R (t)]; and satisfy the constraints: s i S (t) + s i I (t) + s i R (t)=1 (0 ≤ s i * (t) ≤ 1); Si(t) represents the state vector of node i at time t; s i S (t) represents the probability that node i is in a susceptible state (Susceptible) at time t; s i I (t) represents the probability that node i is in the infected state (Infected) at time t; s i R (t) represents the probability that node i is in the recovered state (Recovered) 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.

[0059] The susceptible sub-state (S) indicates that the node is in a state where it is operating normally but has the possibility of risk exposure. Its calculation formula is: s (S) i = (Q cap - |Q in -Qout |) / Q cap × e -λt Where: λ = 0.05h -1 is the environmental risk accumulation rate.

[0060] The infection sub-state indicates the state of risk events such as siltation, ecological deterioration, or exceeding the safe flow rate at the node. Its calculation formula is: i I = 1 / (1+exp(-α·(Δh / h crit +Δt fail / T resp ))); Where: s i I represents the probability that node i is in the infected state (Infected); α is the shape coefficient, which is set to 2.5 and is 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 head deviation threshold; Δt fail Indicates the time after the fault occurs; T resp Indicates the emergency response time threshold.

[0061] The recovery sub-state indicates the state where the risk is eliminated by taking measures such as dredging and ecological restoration. The expression formula is: s i R = tanh(β·∫ t t0 m(τ) dτ); Where: m(τ) is the intensity of maintenance resource input, s i R represents the probability that node i is in the recovered state (Recovered); tanh is the hyperbolic tangent function, which maps the input to the interval (-1,1) and is used here to map the recovery degree to the interval [0,1); β is the recovery efficiency coefficient, which is 0.3 and represents the efficiency of converting maintenance resources into recovery effects; ∫ t0 t m(τ)dτ represents the cumulative investment of maintenance resources from the fault start time t0 to the current time t; m(τ) represents the maintenance resource investment intensity at time τ.

[0062] Based on the initial state of each node determined by expert guidance, the following state transfer differential equations are constructed to represent the transition between states, expressed as: ds i S / dt = -∑ j∈N(i) w ji (t)·s j I si 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)·s i 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 amount of maintenance resources invested; γi(t) represents the immunity decay rate, which is generally taken as 0.01h -1 .

[0063] In summary, a time-varying SIR model at the target level is constructed to simulate the risk propagation within this level, taking time-varying factors into consideration. The establishment of the transition between the sub-states of each node that takes time-varying factors into consideration can better reflect the impact of risks on each node than the general single node state.

[0064] To establish a node-level risk propagation model, we first abstract the real-time status of the node-level nodes into a five-dimensional vector, which is expressed as: V i (t)=[ Q in (t), Q out (t), h res (t), σ(t), τ delay (t)] T ; Where: Q in (t),、 Q out (t) represents the average inflow and outflow flow of the period, in m 3 / s;h res It represents the deviation rate between the water level in front of the dam and the design water level, expressed as a percentage; σ represents the structural health index calculated based on crack width, seepage rate, material fatigue, etc.; τ delay Indicates the emergency response delay time in minutes. The parameter is normalized using the range method.

[0065] Based on the definition of node multi-dimensional state vector and parameter calibration, a dynamic calculation model of directed edge weight is constructed. First, define the edge e ij The basic conductivity coefficient is used to calculate the hydraulic correlation strength, and the calculation formula is: w ij base = (Q* ij ·L ij -0.7 ) / (1+0.3|ΔZ ij |); Where: Q* ij is the average flow rate in 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 meters.

[0066] Fuzzy evaluation indicators are established, trapezoidal membership functions are used to quantify the risk level of each indicator, and the node risk entropy value is obtained through weighted synthesis operators. Then, a reaction-diffusion risk propagation equation is established, which is expressed as: dR j / dt = D j ▽ 2 R j + ∑(i∈Γ j - )α ij R i (t-τ ij ) - β i R j n ; 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 transmission lag; β j =0.03(1-σ j ) represents the natural attenuation rate of risk. Set the risk value of the boundary node and the end node to meet dR / dx=0. The finite volume method is used to discretely solve the risk propagation equation, which is expressed as: R j n+1 = R j n + Δt[D j (R j+1 n -2Rj n +R j-1 n ) / Δx 2 + S j n ]; where: S n j is the source term, including upstream input and self-attenuation; the time step satisfies the CFL stability condition Δt≤Δx 2 / (2D max ).

[0067] In summary, at the node level, multi-state fusion is used to break through the limitations of single-indicator risk assessment and realize multi-physical field coupling; the directional differences in upstream and downstream risk transmission are characterized by time-delay differential equations; and the combination of data-driven fuzzy evaluation and the diffusion equation of physical mechanisms improves the generalization ability of the model.

[0068] On the basis of the risk propagation model at each level, a cross-level risk propagation model is constructed based on the hydraulic connection relationship between the upstream and downstream water systems at the class, order, and knot levels. In this embodiment, a cross-level dominance matrix is ​​first constructed, and the dominance matrix D = [d kl ], the class-order dominance matrix D G-M is a sparse matrix whose non-zero elements satisfy the condition: When the annual water diversion volume of the target node is ≥ 0.5Q Gk , dkl=1, otherwise it is equal to 0.

[0069] D-node dominance matrix D M-J , whose elements represent the dependency of scheduling instructions. A cascade reaction equation system is established to express the risk propagation across levels, which is expressed as follows: 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 ; Where: m mJ = Q mJ / Q 总 m ·e -0.1L Mj represents the propagation coefficient from the eye to the junction layer; h gJ =0.2·A g / A Jrepresents the direct transmission coefficient from the ganglion to the node; t gJ =max(L gm / v gm ,L mJ / v mJ ) represents the calculation of the time lag. The above process represents the forward mechanism from the hierarchy level to the item level to the node level. Now we establish the reverse feedback mechanism, which is defined as follows: ΔR m = ∑ j∈J(m) (dR j / dt)(S j / S m )·cosθ jm ; Where: ΔR m Indicates the risk change of the target level node m, dR j / dt represents the instantaneous change rate of risk of node j at the node level, q jm represents the topological angle between node j and destination node m; S j / S m is the project scale ratio between the node and the destination node.

[0070] ΔR g = ∑ m∈M(g) (dR m / dt)(S m / S g )·cosθ mg ; Where: ΔR g Indicates the risk change of the level node g, dR m / dt represents the instantaneous change rate of risk of target level node m, q mg represents the topological angle between the destination node m and the root node g; S m / S g It is the project scale ratio between the target node and the outline node.

[0071] In this embodiment, a complex network of hierarchy, order, and node levels is first established based on the water network topology. On this basis, risk propagation models of each level are established according to the number of nodes at each level and the characteristics of the risk impact range. A cross-level risk propagation model is established based on the connection relationship between the upstream and downstream water systems. This realizes the correlation study between the water network topology and the risk propagation dynamics, provides a systematic research idea for the study of risk propagation laws of complex water network systems, and provides a research template for watershed risk propagation research.

[0072] According to one aspect of the present application, step S4 is further: Step S41: Conduct 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 attack. Then, 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 impact effects of risks occurring at different levels, a hierarchical amplification factor is set to map the vulnerability nodes and key risk paths between levels, and identify the vulnerability levels and key risk paths of the entire water network system.

[0073] In this real-time example, based on the complex network of each level, the risk propagation model, and the cross-level risk propagation model established in step S3, the vulnerability nodes and key risk paths of each level are analyzed; based on the water system connection relationship between levels and the node level mapping, the vulnerability level of the entire water network system and the key risk paths of the system are analyzed.

[0074] An improved PageRank algorithm is used to perform intelligent local attacks on each level of the complex network, obtaining the set of failed nodes at each level. The initial load of the nodes at the physical network layer is calculated, and a dynamic random attack is performed on the complex network based on a constructed cascade trigger simulation mechanism. During the initial attack, nodes with loads exceeding a threshold are randomly removed. The load of the remaining nodes is updated in real time after each round of attack. This results in a cascading sequence of failed nodes and the degree of fragmentation at each level after the attack. The degree of fragmentation is represented by the calculated fragmentation coefficient. Based on the set of failed nodes formed after the intelligent local and dynamic random attacks and the inter-layer coupling relationship, a coupled percolation model is constructed to obtain the cascading failure path. A Monte Carlo simulation method is used to calculate the critical attack ratio of network connectivity mutations to obtain the percolation threshold. Based on the cascading failure path and percolation threshold, node vulnerability indicators are defined and calculated, resulting in a node vulnerability ranking. An improved random walk algorithm is used to identify key risk propagation paths. Consequently, vulnerable nodes and key risk propagation paths at each level are obtained.

[0075] Based on the functional differences among water network hierarchies, amplification coefficients for risk transfer between hierarchies are defined and calibrated using expert experience. Failure nodes at the framework level are mapped to the item level using the amplification coefficients, and then the item level is mapped to the node level using the amplification coefficients. The vulnerability scores of these superimposed nodes are then calculated. By integrating the critical risk paths at each level, a critical risk transmission path for the water network system is constructed. This analysis yields the critical risk hierarchy and overall critical risk path for the water network system. This analysis analyzes the risk evolution patterns at each level and the risk characteristics of the entire system, facilitating the implementation of targeted risk control measures for vulnerable risk nodes and critical risk paths, maximizing system security and overall benefits.

[0076] According to one aspect of this application, the specific outputs of the present invention include: The vulnerability nodes and key risk paths at the framework, item and node levels in the complex water network system, as well as the vulnerability levels of the complex water network system and the key risk paths of the system as a whole.

[0077] In this embodiment, the above steps are used to obtain the vulnerability nodes and key risk paths of each level in the complex water network system of a certain river basin, and the vulnerability level of the entire water network system and the key risk path of the entire system are obtained, which provides a new solution for identifying the risk evolution law of complex water network systems, and has high innovation and practical significance.

[0078] The preferred embodiments of the present invention are described in detail above. However, the present invention is not limited to the specific details in the above embodiments. Within 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 fall within the scope of protection of the present invention.

Claims

1. A dynamic identification method for the risk evolution law of complex water network system, characterized by: The steps include: Step S1, collecting basic information of water conservancy projects in the water network study area and identifying risk factors to obtain a risk factor sample set; Step S2: divide the water conservancy projects in the water network study area into a three-level hierarchical structure of outline, project and conclusion to construct a multi-objective real-time risk scheduling model, take the risk factor sample set as input and solve it to obtain a risk scheduling plan set; Step S3: Based on the risk scheduling scheme set and the hierarchical structure of the complex water network system, a real-time scheduling risk propagation model for each level is established, the risk propagation mechanism in the hierarchy, item, and structure levels is analyzed in sequence, and the node dominance mapping between levels is established according to the water system connection relationship between levels, so as to obtain a global real-time risk propagation network model; Step S4: Based on the global real-time risk propagation network model, the vulnerable nodes and key risk paths of the hierarchy, order, and node layers are identified respectively, and cross-level node dominance mapping is performed to identify the vulnerable level and key risk path of the entire water network system.

2. The method for dynamically identifying the risk evolution law of a complex water network system according to claim 1 is characterized in that: The step S3 is further as follows: Step S31, reading and establishing a complex network of each layer based on the hierarchical structure, generalizing the water conservancy projects of each layer into nodes, and establishing directed edges between nodes with direct hydraulic connections; Step S32, analyzing the differences in the number of nodes and the scope of influence in each level of the outline, item, and knot, and constructing risk propagation models at each level based on the complex network at each level; Step S33, based on the connection relationship between the upstream and downstream water systems of the water network in the study area, construct a cross-level risk propagation mapping mechanism in which the outline-level nodes map to the dominant item-level nodes, and then the item-level nodes map to the dominant node-level nodes, to construct a cross-level risk propagation network model.

3. The method for dynamically identifying the risk evolution law of a complex water network system according to claim 2 is characterized in that: The step S32 is further as follows: Step S32a: Establish a pressure wave propagation dynamics model for simulating risk propagation at the level of the network, calculate the failure influence of each node and sort it; Step S32b: Establish a time-varying SIR model for the target level, divide each node state into a susceptible sub-state, an infected sub-state, and a recovered sub-state, and at each moment, the sum of the weights of each node sub-state is 1; Step S32c: establish an asymmetric risk diffusion model for simulating risk propagation at the node level, and the weight of the directed edge between nodes represents the risk transmission intensity.

4. The method for dynamically identifying the risk evolution law of a complex water network system according to claim 1 is characterized in that: The step S4 is further 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 risks occurring between levels, the level magnification coefficient is set to map the vulnerability nodes and key risk paths between levels, and the vulnerability levels and key risk paths of the entire water network system are identified.

5. The method for dynamically identifying the risk evolution law of a complex water network system according to claim 4 is characterized in that: The step S41 is further as follows: Step S41a, calculating the node attack priority based on the node topology attributes and dynamic weights, giving priority to attacking nodes whose node topology attributes are higher than a preset threshold, and generating a local attack failure node set; Step S41b: adaptively adjust the attack frequency according to the real-time status of the network, 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 dynamic attack failure node sets, calculate the node impact factor through the vulnerability quantification model, and combine the propagation path discovery to obtain the vulnerability nodes and key risk paths at each level.

6. The method for dynamically identifying the risk evolution law of a complex water network system according to claim 4 is characterized in that: The step S42 is further as follows: Step S42a: Based on the hierarchical topological structure of the water network system, a risk transfer matrix is ​​established to analyze the coupling effect between adjacent levels, thereby setting the risk amplification factor of the level; Step S42b: Mapping the hierarchical vulnerability nodes and key risk paths based on the hierarchical risk amplification factor to identify the vulnerability level and key risk paths of the entire water network system.

7. The method for dynamically identifying the risk evolution law of a complex water network system according to claim 1 is characterized in that: The step S1 is further as follows: Step S11, collecting basic information of water conservancy projects in the water network study area, identifying risk factors therefrom, and screening out a risk factor set; Step S12, reading the risk factor set and grouping the risk factor set using a spectral clustering method with balanced inter-group scale, and constructing risk factor distributions for the associated risk factors and the unassociated risk factors of each group, including the joint distribution of the associated risk factors and the distribution of the unassociated risk factors; Step S13: Generate a sample set of risk factors according to the risk factor distribution, use the entropy regularized Wasserstein optimal transmission algorithm to obtain a mixed sample set aligned in time and space, and perform verification and correction to obtain a risk factor sample set.

8. The method for dynamically identifying the risk evolution law of a complex water network system according to claim 7 is characterized in that: The step is a spectral clustering method for balancing the scales between groups in S12, specifically: Based on the risk factor set, identify the correlated risk factors and uncorrelated risk factors; By setting the number constraints of group size and intra-group correlation risk factors, the risk factors of the classification clusters are tested and adjusted to obtain the risk factor set grouping.

9. The method for dynamically identifying the risk evolution law of a complex water network system according to claim 1 is characterized in that: The step S2 is further as follows: Step S21, divide the water conservancy projects in the water network study area into a three-level hierarchical structure of outline, target, and conclusion to construct a multi-objective real-time risk scheduling model, where the outline level is major water diversion and regulation projects, the target level is river-lake connection projects and water transmission and distribution projects, and the conclusion level is water conservancy hub projects including reservoirs and pumping stations; Step S22: Taking the risk factor sample set as input, the objective function of each level is mapped into a quantum bit superposition state, and the relationship between levels is established through the entanglement mechanism to generate a risk scheduling plan set.

10. The method for dynamic identification of risk evolution law of complex water network system according to claim 9 is characterized in that: In step S21, the objective function and constraint conditions of the multi-objective real-time risk scheduling model are specifically: The objectives of the framework level are to minimize water diversion risks, ecological impacts and economic costs; the objectives of the project level are to minimize comprehensive risks, economic costs and maximize water supply benefits; and the objectives of the structure level are to minimize comprehensive risks, operating costs and maximize comprehensive benefits. The constraints include water transfer capacity constraints and water balance constraints at the framework level, engineering water transfer capacity constraints, hydraulic connection constraints, river ecological flow constraints, and water supply guarantee constraints at the project level, and water balance constraints, equipment capacity constraints, hydraulic coupling constraints, and flood control point safety constraints at the structure level. Based on the objective functions and constraints at each level, a multi-objective real-time risk scheduling model is constructed.

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