Urban coordinated development assessment method based on water resources and coupling factors thereof

Abstract

The invention provides an urban coordinated development evaluation method based on water resources and coupling factors thereof, and belongs to the technical field of development evaluation based on deep learning. The method comprises the following steps: firstly, constructing a structured data set covering a ternary system, and introducing a physical quantization tag to ensure the objectivity of an evaluation result; secondly, designing a causal modeling network with a two-level structure, fusing system-level and index-level contribution analysis mechanisms, and realizing structured mining of a coupling causal relationship; then, through a model structure inversion mechanism, proposing a three-item multi-dimensional index system for evaluating the potential, coordination and stability of urban development; and finally, in combination with structure prior information and an evaluation result, constructing a game theory-driven multi-round regulation and control path deduction framework, and realizing automatic generation of a collaborative variable regulation and control scheme and prediction and evaluation of a development effect, thereby providing high-quality collaborative development path suggestions with reasonability and mechanism interpretability for cities.

Description

Technical Field

[0001] This invention belongs to the field of development evaluation technology based on deep learning, and in particular relates to an assessment method for coordinated urban development based on water resources and their coupling factors. Background Technology

[0002] As complex entities where multidimensional systems converge, the sustainable development of cities largely depends on the dynamic balance between natural resource carrying capacity, social system operation, and ecological environment stability. Especially against the backdrop of increasingly tight resource and environmental constraints and rising demands for development quality, water resource security, socio-economic growth potential, and ecosystem stability have become key factors influencing a city's comprehensive development capacity. While the operational mechanisms, modes of action, and regulatory responses of these three subsystems differ, they exhibit strong coupling and highly interconnected integrated characteristics within urban space. The nonlinear interactions between these systems not only determine the current state of urban development but also profoundly influence the feasibility and stability of future paths. Comprehensively identifying and understanding the inherent synergistic relationships, developmental tensions, and structural potential among these systems has become a core task in urban development planning and governance.

[0003] Currently, the comprehensive assessment of coordinated urban development mainly includes the following methods:

[0004] Multi-indicator comprehensive evaluation method: This method standardizes and linearly weights indicators from multiple dimensions such as urban water resources, socio-economic conditions, and ecological environment by setting an indicator system and weighting rules to generate a comprehensive score to characterize the level of coordinated urban development. Although simple to implement and intuitive in results, its weights usually rely on expert experience and lack objective basis. Furthermore, it is difficult to reveal the coupling relationship and causal mechanism between indicators, and the evaluation results lack structural explanatory power and reasoning ability.

[0005] Urban system dynamics modeling: This type of method treats the city as a dynamic feedback system composed of multiple variables, using differential equations to describe the evolutionary relationships between these variables, thereby predicting urban development trends and coordination through simulation. While this method can reflect macroscopic evolutionary processes, its modeling relies heavily on strong prior assumptions and parameter settings, lacking flexibility and adaptability. Furthermore, its coarse-grained modeling makes it difficult to accurately identify key regulatory indicators or finely model the system's coupling structure.

[0006] Machine learning-based prediction and evaluation methods: Machine learning methods utilize large-scale historical data to train supervised models to predict and evaluate the level of coordinated urban development. Commonly used models include random forest, XGBoost, and LSTM. Although they have high predictive power, these methods are often "black box models," lacking the ability to analyze the causal structure of indicators, unable to generate reverse control strategies, and struggling to cope with the coupling complexity between multiple subsystems. Their interpretability and decision support value are limited.

[0007] In summary, although existing urban coordinated development assessment technologies have made some progress in terms of indicator integration, system modeling, and data-driven prediction, they generally suffer from problems such as weak structural explanatory power and lack of causal mechanism modeling. Summary of the Invention

[0008] To address the above problems, this invention proposes a method for assessing coordinated urban development based on water resources and their coupling factors, comprising the following steps:

[0009] S1: Collect structural characteristic indicators of three subsystems covering the target urban area: water resources, socio-economic and ecological environment, and construct a structured dataset for modeling coordinated urban development; extract representative indicators from the subsystems as input features, and use coordinated development labels composed of quantifiable physical indicators as output;

[0010] S2, construct a hierarchical coupling contribution modeling network model for the urban system, including a first-level system-level impact analysis network and a second-level indicator-level coupling modeling network. The former captures the heterogeneous semantic relationships between subsystems and generates system-level feature representations F. Ss The latter constructs the original graph structure data based on the input indicator data, extracts node interaction representations, and fuses them to generate the hierarchical coupling contribution feature F. Sm Based on the first-level output F Ss With secondary output F Sm The predicted results of urban coordinated development indicators were obtained; the model was trained using the dataset collected by S1.

[0011] S3. After the model is trained, its structural interpretability is used to conduct a multi-dimensional inversion assessment of the city's coordinated development status: Based on the expected coordinated development indicators, the minimum indicator disturbance cost required to achieve the target development status is calculated through the strategy inversion mechanism, forming the system strategy inversion assessment index SSI; Based on the response behavior of the trained model and its internal subsystems, simulation regulation and consistency inference are carried out to output the system coordination degree assessment index CoD; Based on the structure of the trained model and its causal mapping mechanism, the system transferability index is constructed to obtain the city development stability assessment index TL.

[0012] Preferably, the process also includes the following:

[0013] Based on the hierarchical coupling contribution modeling network model of the urban system obtained from S2, the global impact contribution between systems is modeled based on the first-level system-level impact analysis network, and the marginal impact and cross-coupling relationship of the input indicators are modeled based on the second-level indicator-level coupling modeling network, resulting in the system-level impact index V reflecting the contribution of system-level data. sl Marginal contribution map V, reflecting the contribution of indicator-level data. ecAnd the coupling strength matrix GT, which reflects the coupling degree at the indicator level;

[0014] Based on the output evaluation results, a game reasoning framework is constructed to recommend multi-round urban coordinated development regulation paths; water resources, socio-economic and ecological environment systems are treated as independent game subjects, and a game cost function is constructed with three-dimensional evaluation indicators; a graph-guided game mechanism is used to iteratively generate perturbation sequences and seek optimization, and finally output an interpretable coordinated development regulation path.

[0015] Preferably, the water resources subsystem index WS includes: per capita water resources WS pc Water production modulus WS pm Groundwater supply ratio (WS) gs Industrial water usage percentage (WS) pi Agricultural irrigation water volume WS ai Water resource development and utilization rate (WS) du Water resource utilization efficiency (WS) ue Annual average precipitation WS ap ;

[0016] The socioeconomic subsystem indicators include SE, which includes: GDP per capita. pc The proportion of primary / secondary / tertiary industries (SE) fp SE sp SE tp Total fixed asset investment SE tf Population density SE pd Urbanization rate (SE) ur Total retail sales of consumer goods (SE) tr Public finance expenditure ratio SE fe ;

[0017] The ecological environment subsystem indicator EE includes: green coverage rate of built-up areas EE gu Solid waste comprehensive utilization rate EE sw Wastewater discharge per 10,000 yuan of GDP (EE) wd Carbon emissions per unit area (EE) ce Wastewater treatment rate EE st Number of days with acceptable air quality (EE) eq Ecological red line ratio EE rl .

[0018] Preferably, quantifiable physical indicator labels include the Resource-Environment Carrying Capacity Index (DV). rc Green Development Index (DV) gd Regional Coordinated Development Index (DV) ac Urban Sustainable Development Capacity Index (DV) cs .

[0019] Preferably, the hierarchical coupling contribution modeling network model of the urban system is specifically as follows:

[0020] The first-level system-level impact analysis network transforms the indicator data of the three subsystems through two fully connected layers, and uses layer normalization and ReLU activation function to enhance the nonlinear expressive power of the features. Subsequently, a Dropout layer is used to enhance the model's generalization ability. The transformed feature vectors of the three types are fused through a multi-dimensional heterogeneous perceptual attention layer to capture the heterogeneous semantic relationships between subsystems and generate a system-level feature representation, denoted as the system structure feature F. Ss ;

[0021] The second-level index-level coupling modeling network first uses all index data as input without partitioning; then, each index is represented as a node, and edges are constructed based on prior knowledge for possible coupling relationships to obtain the original graph structure data; finally, node interaction representations are extracted through two layers of graph attention network and denoted as graph structure features F. Gs Then it branches into two:

[0022] Marginal contribution modeling branch: F Gs The input is fed into a multilayer perceptron, then into a conditional attribution attention layer to capture the marginal importance of different indicators, and the output is a representation of the marginal influence of the indicators, F. Me ;

[0023] Interactive coupling modeling branch: F Gs After inputting into a multilayer perceptron, multi-level interaction modeling is performed through a CrossNet cross-feature encoding layer, outputting coupled interaction features F. Ci ;

[0024] The two branch outputs are dynamically fused through a gating fusion mechanism to generate the hierarchical coupling contribution feature F. Sm ;

[0025] Finally, the first-level output F Ss With secondary output F Sm By stitching and fusing through fully connected layers and mapping to the coordinated development label space using the ReLU activation function, the final predicted result DV of the urban coordinated development index is obtained. pre .

[0026] Preferably, the specific process for obtaining the System Strategy Inversion Evaluation Index (SSI) is as follows:

[0027] First, set a set of expected urban coordinated development indicators (DV). best Use the trained model and freeze the model parameters and structure;

[0028] Secondly, the three subsystem indicators WS, SE and EE are concatenated as the complete input data Cod, which is used as the initial data x0. The controllable indicator variables are selected as optimization variables to generate multiple control data x′.

[0029] The optimization objective is set as minimizing the sum of the control achievable loss and the control cost; where the control achievable loss is the sum of the urban coordinated development forecast result obtained with control data x′ as input and the DV. best The mean square error between the control data x′ and the initial data x0 is taken as the control cost, which is the L1 norm between the control data x′ and the initial data x0. With this as the objective, the L-BFGS optimizer is selected to search for the minimum perturbation input vector x that satisfies the target output. * ;

[0030] Then, calculate x * The L2 norm, which differs from x0, serves as the strategic intervention cost for adjusting the city's state, i.e., the system strategy inversion evaluation index (SSI).

[0031] Preferably, the specific process for obtaining the system coordination degree evaluation index CoD is as follows:

[0032] For the first-level system-level influence analysis network of the trained model, firstly, the response features FS1, FS2, and FS3 of the first three systems entering the multidimensional heterogeneous perception attention layer are recorded when the complete input data Cod is used as input. Then, a small perturbation is applied to the input index of any one of the three systems, while the inputs of the other two systems remain unchanged. The training model is then run once to obtain the response features FS'1, FS'2, and FS'3 after adjusting the input. Finally, the partial derivative between the response of the p-th fixed subsystem and the q-th perturbation subsystem is calculated to obtain the cross-system influence mapping tensor R. q→p And p,q∈[1,3];

[0033] Extensive testing was conducted on each subsystem, and the results were averaged to obtain the complete cross-system impact mapping matrix R; subsequently, the reciprocity consistency r was calculated. qp The mutual consistency calculation results r between each pair of the three systems are obtained. 12 r 13 r 23 Finally, the average of the three is taken as the system coordination degree CoD evaluation result, and CoD∈[0,1].

[0034] Preferably, the specific process for obtaining the urban development stability assessment index TL is as follows:

[0035] Using the original structure of the S2 model after freezing parameters, masking simulation is performed on each subsystem in the input sample in turn, that is, all input indicators under the subsystem are replaced with missing states to construct pseudo-input samples; at the same time, the original inputs of the other two subsystems are kept unchanged.

[0036] Then, the modified input samples are re-inputted into the trained model to obtain the predicted output, and the deviation Δ between the predicted output and the full input predicted value is calculated. k Then use Δ k The reciprocal of the ratio to the original predicted output is used as the transferability index TLk of the k-th subsystem. This index reflects whether other subsystems can compensate for the impact on the overall coordinated development of the city when a certain type of subsystem fails. k ∈[0,1],TL k The larger the value, the higher the system stability and risk response capability. Ultimately, the transferability index TL of the three subsystems will be... k The average value is used to obtain the city's overall development stability assessment index TL.

[0037] Preferably, the system-level impact index result V sl The acquisition process is as follows:

[0038] For the first-level system-level impact analysis network, a system-level contribution structure mapping process is constructed: First, the attention weight tensors of three types of subsystems are extracted from the multi-dimensional heterogeneous perception attention layer, and then normalized to form the subsystem structure contribution vector V. sc This vector reflects the degree of global impact of different subsystems on the prediction of coordinated urban development under multiple rounds of attention.

[0039] Secondly, a distributed response mapping mechanism is introduced: after subjecting the original subsystem input to a uniform amplitude incremental perturbation, a new output result is obtained through model inference, and the relative change rate of the model output relative to the original output is defined as the system perturbation response intensity V. sd ;

[0040] Finally, using the system disturbance response strength V sd This represents the overall robustness of the model against interference, multiplied by a preset interference weight α. sd Added to the system structure contribution vector V sc In the process, the system-level impact index result V was obtained. sl .

[0041] Preferably, the marginal contribution map V of the indicator ec The process of obtaining the coupling strength matrix GT is as follows:

[0042] We analyze the second-level indicator-level coupled modeling network and construct an indicator-level parsing framework with two dimensions: marginality and interaction.

[0043] Marginal contribution modeling path: Extract the trained normalized attention weight vector V from the output of the marginal contribution modeling branch of the second-level modeling network. wnThis directly reflects the strength of the model's response to different input indicators;

[0044] Simultaneously, combining the nonnegativity and sparsity regularization terms introduced in the model structure, V wn Perform structural attribution deconstruction to generate an indicator marginal contribution map V. ec ;

[0045] Interactive coupling modeling path: Extracting cross-feature vectors from the CrossNet layer output based on the interactive modeling branch in the second-level network. This represents the cross-feature vector between the i-th and j-th indicators;

[0046] After that, Calculate the L2 norm to obtain the joint feature expression strength between the two indicators. The larger the value, the stronger the interactivity, and this value is used as the indicator of coupling strength. By quantifying the cross-coupling strength of each pair of indicators in model inference, the complete coupling strength matrix GT between indicator pairs is finally constructed.

[0047] Preferably, based on the output evaluation results, a game theory reasoning framework is constructed to recommend multi-round urban coordinated development regulation paths. The specific process is as follows:

[0048] Collaborative graph construction and variable selection: First, define the current state z0 of the city as the initial state, and combine it with the marginal contribution graph V. ec The Top-K strategy is used to select K input indicators with the greatest contribution, and a set of control variables, Set, is obtained. con Secondly, the indicators in the set of control variables are used as nodes, and the coupling degree between any two indicators in the coupling strength matrix GT is multiplied by the contribution degree V of the system to which that indicator belongs. sl As edge features, the initial collaborative graph is obtained; where nodes represent control variables and edges represent the overall coupling strength.

[0049] Multi-party game modeling: Three types of urban subsystems are treated as independent game participants, namely: A1, A2, and A3; each subsystem is represented by a set of control variables. con Select a subset of the control variables associated with itself as the strategy space, namely Set1, Set2, Set3; and construct the game cost function Loss as the sum of the mean square errors between the current system strategy inversion index assessment SSI, system coordination degree assessment CoD, and urban development stability assessment TL and the three assessments corresponding to the game deduction generation path.

[0050] Interpretable path reasoning and optimization guided by cooperative graph: Based on the adjacency matrix and edge weight information of the cooperative graph structure, the indicators in the control variable set are sorted by graph structure through the path with the maximum coupling degree, thereby determining the perturbation priority sequence Seris;

[0051] Subsequently, in each round of game iteration, Seris prioritizes key variables to regulate z0 according to the priority sequence, generating regulation scheme z1. The quality of the generated regulation scheme z1 is then evaluated using the game cost function Loss of S4-2. A graph-guided game update mechanism is employed to update the adjustment order and magnitude of strategies among variables. By minimizing the game cost function Loss, the regulation strategy is continuously updated until iterative convergence to an approximate Nash equilibrium point, ultimately generating the optimal regulation path z. best This refers to the coordinated urban development path that meets the overall system's regulatory objectives.

[0052] Compared with the prior art, the present invention has the following beneficial effects:

[0053] (1) Structural interpretability causal modeling framework for ternary systems: A hierarchical coupling contribution modeling network model for urban systems containing two-level networks was constructed. This model not only outputs the contribution evaluation results at the system level, but also generates the marginal contribution map and coupling strength matrix at the indicator level. It has the characteristics of strong structural interpretability and transparent action path, laying the foundation for subsequent inversion evaluation and path reasoning.

[0054] (2) Multidimensional Coordination Evaluation System Based on Structural Inversion: This invention differs from traditional static comprehensive evaluation methods by designing an inversion evaluation mechanism based on a hierarchical coupled contribution modeling network structure, and constructing a three-dimensional index system of urban system development potential, coordination, and stability. This evaluation system directly utilizes the internal structure of the model to perform state simulation and inversion of control results, without relying on human experience to set weights or subjective scoring, thus realizing a structurally driven, self-explanatory, and global quantitative evaluation of urban development status.

[0055] (3) Integrating Game Theory Reasoning and Graph Structure-Guided Explainable Path Recommendation Mechanism: This invention proposes a graph-guided game theory reasoning strategy generation engine. It constructs a collaborative graph using marginal contribution graphs and coupling strength matrices, and builds a cost function by combining the target deviations of three types of subsystems, driving the priority ranking and game-based updates of urban regulation variables. This strategy utilizes both structural priors and evaluation feedback, possessing high interpretability and path optimization capabilities. Attached Figure Description

[0056] Figure 1 This is a flowchart illustrating the overall implementation process of the present invention.

[0057] Figure 2 A network model structure diagram is provided to contribute to the modeling of hierarchical coupling in urban systems.

[0058] Figure 3 Flowchart for the module of coordinating development path recommendation and effectiveness prediction.

[0059] Figure 4 This is a comparison chart of green development index predictions in the examples.

[0060] Figure 5 This is a comparison chart of the predicted urban sustainable development capacity index in the examples.

[0061] Figure 6 The diagram shows the mutual consistency evolution of the ternary system in the embodiment.

[0062] Figure 7 The graph shows the change in the stability index under the subsystem failure simulation in the example.

[0063] Figure 8 This is a diagram showing the control variable disturbance path and priority in the example.

[0064] Figure 9 This is a comparison chart of the predicted coordinated development indicators under the original state and the control path in the embodiment. Detailed Implementation

[0065] This invention proposes an assessment method for coordinated urban development based on the coupling of water resources, socio-economic factors, and the ecological environment. The overall technical route flowchart is as follows: Figure 1 As shown, the method includes:

[0066] The ternary system index dataset construction module collects structural characteristic indicators of three subsystems covering the target urban area: water resources, socio-economic and ecological environment, and constructs a structured dataset for urban coordinated development modeling. Specifically, it includes: acquiring core observation data through multi-source data channels, extracting representative indicators from the three subsystems as input features, and using coordinated development labels composed of quantifiable physical indicators as output, thereby forming a ternary system structured dataset with supervised modeling capabilities.

[0067] A hierarchical coupling contribution modeling network for urban systems is designed based on a constructed dataset. This model features a hierarchical structure and a coupling awareness mechanism, including a first-level system-level impact analysis network and a second-level indicator-level coupling modeling network. This model models the structured mapping process of the three-dimensional subsystems towards coordinated development goals. The collected dataset is used to train the model. After training, the first-level system-level impact analysis network models the global impact contribution between systems, while the second-level indicator-level coupling modeling network simultaneously models the marginal impact and cross-coupling relationships of the input indicators. The system-level impact indicator result V is then obtained. sl (Reflecting the contribution of system-level data), indicator marginal contribution map V ec(Reflecting the contribution of indicator-level data), and the coupling strength matrix GT (reflecting the coupling degree of indicator-level data).

[0068] Urban Coordinated Development Inversion Assessment: After the model is trained, its structural interpretability is utilized to conduct a multi-dimensional inversion assessment of the state of urban coordinated development. This includes: calculating the minimum indicator disturbance cost required to achieve the target development state through a strategy inversion mechanism, forming the strategy inversion assessment index SSI; calculating the coordination of each subsystem based on the model's response differences, outputting the system coordination degree assessment index CoD; and assessing the functional substitutability between subsystems under input-missing simulations, quantifying it to form the urban development stability assessment index TL.

[0069] Recommendations for Coordinated Development Paths and Predictions of Outcomes: Based on System-Level Impact Indicator Results V sl Marginal contribution map of indicators V ec The system uses a coupling strength matrix GT, combined with the system strategy inversion evaluation index SSI, the system coordination degree evaluation index CoD, and the urban development stability evaluation index TL. It treats water resources, socio-economic and ecological environment systems as independent game subjects and constructs a game cost function with three-dimensional evaluation indicators. It uses a graph-guided game mechanism to iteratively generate disturbance sequences and seek optimization, and finally outputs an interpretable coordinated development regulation path. The recommended path is input into the training model to predict the effectiveness of urban coordinated development, realizing a closed loop of path effect evaluation and structural optimization.

[0070] The specific implementation process of the present invention will be further described below with reference to specific embodiments.

[0071] I. Construction of the Triad System Indicator Dataset

[0072] To comprehensively characterize the features of the three subsystems—water resources, socio-economic, and ecological environment—in the process of coordinated urban development and to achieve quantifiable evaluation of multidimensional information, this invention first collected multi-source heterogeneous data of the three-element system. Furthermore, to reflect the true state of coordinated urban development, corresponding urban development status labels were established for the input data of the three-element system, ultimately obtaining a dataset of three-element system indicators with input-output mapping relationships. Specifically, the following steps are included:

[0073] Data collection sources: Based on the observation needs of the three subsystems of water resources, socio-economic and ecological environment, we have determined the multi-source data channels that can be used for collection, including: urban statistical yearbooks, government work reports, land use monitoring results, and IoT facilities such as groundwater monitoring stations, to obtain real-time observation data;

[0074] Three-dimensional system indicator collection: Based on the determined data sources, core structural indicators from the three subsystems are collected, including:

[0075] (1) The water resources subsystem index WS includes: per capita water resources WS pc Water production modulus WS pm Groundwater supply ratio (WS) gs Industrial water usage percentage (WS) pi Agricultural irrigation water volume WS ai Water resource development and utilization rate (WS) du Water resource utilization efficiency (WS) ue Annual average precipitation WS ap That is: WS = [WS pc WS pm WS gs WS pi WS ai WS du WS ue WS ap ];

[0076] (2) Socioeconomic subsystem indicators include: SE (GDP per capita) pc The proportion of primary / secondary / tertiary industries (SE) fp SE sp SE tp Total fixed asset investment SE tf Population density SE pd Urbanization rate (SE) ur Total retail sales of consumer goods (SE) tr Public finance expenditure ratio SE fe ;That is: SE=[SE pc SE fp SE sp SE tp SE tf SE pd SE ur SE tr SE fe ];

[0077] (3) The ecological environment subsystem index EE includes: green coverage rate of built-up area EE gu Solid waste comprehensive utilization rate EE sw Wastewater discharge per 10,000 yuan of GDP (EE) wd Carbon emissions per unit area (EE) ce Wastewater treatment rate EE st Number of days with acceptable air quality (EE) eq Ecological red line ratio EE rl ;That is, EE=[EE gu EE sw EE wd EE ce EEst EE eq EE rl ];

[0078] Urban Coordinated Development Labeling: To ensure that the constructed ternary system indicator dataset has a clear supervised modeling objective and can comprehensively reflect the state of urban coordinated development, this invention selects four comprehensive, quantitatively stable physical labeling indicators for coordinated development, namely: Resource-Environmental Carrying Capacity Index (DV). rc Green Development Index (DV) gd Regional Coordinated Development Index (DV) ac Urban Sustainable Development Capacity Index (DV) cs ;

[0079] Therefore, the urban coordinated development label DV = [DV] rc DV gd DV ac DV cs ];

[0080] Construction of a structured dataset for a three-element system: Using three types of subsystem indicators WS, SE, and EE as inputs and the urban coordinated development label DV as output, a set of structured datasets for a three-element system is obtained. Based on this method, extensive data collection is carried out to obtain a complete structured dataset for a three-element system.

[0081] II. Design and Data Processing of a Hierarchical Coupling Contribution Model for Urban Systems

[0082] To achieve structured modeling of the urban coordinated development goals through a three-dimensional subsystem, this invention constructs a hierarchical coupling contribution modeling network model for urban systems with hierarchical structure and coupling perception capabilities. This model consists of a first-level system-level impact analysis network (referred to as the first-level network) and a second-level indicator-level coupling modeling network (referred to as the second-level network). The first-level network models the system-level impact relationships of the three subsystems—water resources, socio-economic, and ecological environment—on the urban coordinated development goals. The second-level network further characterizes the marginal impacts and cross-system interaction coupling mechanisms between multi-dimensional indicators within the subsystems, outputting interpretable, fine-grained indicator contribution analysis results. The model structure is as follows: Figure 2 As shown.

[0083] 1. Network Model Design: This network takes three subsystem indicators (WS, SE, and EE) as inputs and urban coordinated development indicator labels as outputs, and models their mapping relationships step by step through a hierarchical structure; specifically:

[0084] (1) For the first-level network, the indicator data of the three subsystems are transformed through two fully connected layers, and layer normalization and ReLU activation function are used to improve the nonlinear expression of the features; then, the generalization ability of the model is enhanced through the Dropout layer. The transformed feature vectors of the three types are fused through a multi-dimensional heterogeneous perceptual attention layer (this layer is based on the multi-head attention mechanism) to capture the heterogeneous semantic relationships between the subsystems and generate system-level feature representations, denoted as system structural features F. Ss ;

[0085] (2) For the second-level network, all indicator data (including the three subsystem indicators WS, SE, and EE) are first used as input without partitioning; then, each indicator is represented as a node, and edges are constructed based on prior knowledge for possible coupling relationships to obtain the original graph structure data; then, the node interaction representation is extracted through a two-layer graph attention network (GAT) layer and denoted as the graph structure feature F. Gs Then it branches into two:

[0086] Marginal contribution modeling branch: F Gs The input is fed into a multilayer perceptron, then into a conditional attribution attention layer (which utilizes a self-attention mechanism) to capture the marginal importance of different indicators, and outputs a representation of the marginal influence of the indicators, F. Me ;

[0087] Interactive coupling modeling branch: F Gs After inputting into a multilayer perceptron, multi-level interaction modeling is performed through a CrossNet cross-feature encoding layer, outputting coupled interaction features F. Ci ;

[0088] The two branch outputs are dynamically fused through a gating fusion mechanism to generate the hierarchical coupling contribution feature F. Sm That is: the total output features of the second-level modeling;

[0089] (3) Finally, output F of the first stage Ss With secondary output F Sm By stitching and fusing through fully connected layers and mapping to the coordinated development label space using the ReLU activation function, the final predicted result DV of the urban coordinated development index is obtained. pre .

[0090] 2. Model Training: A hierarchical coupling contribution modeling network for urban systems is trained using a constructed ternary system structured dataset. The optimization objective is to minimize the prediction result DV. pre The error between the actual physical label DV and the actual physical label DV is calculated. The optimizer uses Adam and is trained until the error stabilizes and converges, finally obtaining the trained hierarchical modeling network model of the urban system.

[0091] 3. System-level impact mapping generation: Based on the trained urban system hierarchical modeling network, a system-level contribution structure mapping process is constructed for the first-level system-level impact analysis network.

[0092] First, attention weight tensors for three types of subsystems are extracted from the multidimensional heterogeneous perceptual attention layer, and then normalized to form the subsystem structure contribution vector V. sc This vector reflects the degree of global impact of different subsystems on the prediction of coordinated urban development under multiple rounds of attention.

[0093] Secondly, to enhance the interpretability of the system-level causal structure, a distributed response mapping mechanism is further introduced: the original subsystem input is subjected to a uniform incremental perturbation (increased by 5%), and a new output result is obtained through model inference. The relative change rate of the model output with respect to the original output is defined as the system perturbation response intensity V. sd ;

[0094] Finally, using the system disturbance response strength V sd This represents the overall robustness of the model against interference, multiplied by a preset interference weight α. sd Added to the system structure contribution vector V sc In the process, the system-level impact index result V was obtained. sl This reflects the overall impact of each system on the coordinated development of the city;

[0095] 4. Indicator-level Coupled Modeling Analysis: Based on the trained hierarchical modeling network of the urban system, this paper analyzes the second-level indicator-level coupled modeling network and constructs an indicator-level analytical framework with two dimensions: marginality and interaction.

[0096] (1) Marginal contribution modeling path: measuring the strength of the independent effect of each input indicator on the urban coordinated development score,

[0097] Extract the trained normalized attention weight vector V from the output of the marginal contribution modeling branch of the two-level modeling network. wn It directly reflects the strength of the model's response to different input indicators.

[0098] Simultaneously, combining the nonnegativity and sparsity regularization terms introduced in the model structure, V wn Perform structural attribution deconstruction to generate an indicator marginal contribution map V. ec It is used to map the marginal impact of each indicator on the level of coordinated development in the current region.

[0099] (2) Interactive Coupling Modeling Path: To quantify the nonlinear interaction effects between different indicators, this path extracts the cross-feature vectors output by the CrossNet layer based on the interactive modeling branch in the second-level network. This represents the cross-feature vector between the i-th and j-th indicators;

[0100] After that, Calculate the L2 norm to obtain the joint feature expression strength between the two indicators. The larger the value, the stronger the interactivity, and this value is used as the indicator coupling strength. By quantifying the cross-coupling strength of each pair of indicators in the model inference, the complete coupling strength matrix GT between the indicator pairs is finally constructed to reflect the potential coupling relationship between multiple indicators in the process of coordinated urban development.

[0101] Therefore, the final results include the system-level impact index result V. sl (Reflecting the contribution of system-level data), indicator marginal contribution map V ec (Reflecting the contribution of indicator-level data), and the coupling strength matrix GT (reflecting the coupling degree of indicator-level data).

[0102] III. Urban Coordinated Development Inversion Assessment

[0103] To conduct multi-dimensional numerical assessments of coordinated urban development, this invention constructs an urban development assessment strategy system based on a trained hierarchical modeling network model of the urban system and a model structure inversion mechanism. This ultimately results in a structure-driven, multi-dimensional assessment. This scoring system enables reasoned quantitative analysis and structurally interpretable assessment of urban development levels, specifically including the following:

[0104] 1. System Strategy Inversion Index (SSI) Assessment: First, a set of expected urban coordinated development indicators (DV) is set. best Then, the trained urban system hierarchical coupling contribution modeling network was used, and the model parameters and structure were frozen.

[0105] Secondly, the three subsystem indicators WS, SE and EE are concatenated as the complete input data Cod, which is used as the initial data x0. The controllable indicator variables (such as water resource development and utilization rate and green coverage rate of the area) are selected as optimization variables to generate multiple control data x′.

[0106] The optimization objective is set as minimizing the sum of the control achievable loss and the control cost; where the control achievable loss is the sum of the urban coordinated development forecast result obtained with control data x′ as input and the DV. best The mean square error between the control data x′ and the initial data x0 is taken as the control cost, which is the L1 norm between the control data x′ and the initial data x0. With this as the objective, the L-BFGS optimizer is selected to search for the minimum perturbation input vector x that satisfies the target output. * ;

[0107] Then, calculate x *The L2 norm of the difference from x0 serves as the strategic intervention cost for adjusting the city's state, i.e., the System Strategy Inversion Index (SSI). This evaluation index reflects the minimum structural adjustment cost required for a city to achieve its target level of coordinated development, thereby reflecting the city's development potential.

[0108] 2. System Coordination Degree (CoD) Assessment: This assessment measures the coordination and cooperation capabilities of various subsystems in the process of achieving urban development goals. It is based on a trained hierarchical coupling contribution modeling network of the urban system and the response behavior of its constituent subsystems, and conducts simulation regulation and consistency inference.

[0109] Specifically, for the first-level network of the trained model, firstly, the response features FS1, FS2, and FS3 of the first three systems entering the multidimensional heterogeneous perception attention layer are recorded when the complete input data Cod is used as input. Then, a small perturbation is applied to the input index of any one of the three systems, while the inputs of the other two systems remain unchanged. The trained urban system hierarchical coupling contribution modeling network model is then run once to obtain the adjusted response features FS1, FS2, and FS3. Finally, the partial derivative between the response of the p-th fixed subsystem and the q-th perturbation subsystem is calculated to obtain the cross-system influence mapping tensor R. q→p (represents the mapping tensor caused by perturbing the q-th perturbation subsystem to the p-th subsystem), and p, q∈[1, 3];

[0110] Based on this method, extensive testing was conducted on each subsystem, and the results were averaged to obtain the complete cross-system impact mapping matrix R; then, the reciprocity consistency r was calculated based on the following formula. qp :

[0111]

[0112] Where ∈ represents the regularization term, and max(·) is the maximum value operation; and r qp The closer the value is to 1, the more consistent the influence of the two systems is; therefore, the result r of the mutual consistency calculation between each pair of the three systems is obtained. 12 r 13 r 23 Finally, the average of the three is taken as the CoD evaluation result of the system coordination degree, and CoD∈[0,1]. The larger the CoD, the higher the coordination degree among the three systems.

[0113] 3. Urban Development Stability (TL) Assessment: This assesses the development stability of an urban system under conditions of missing local inputs or system malfunctions. It utilizes a trained hierarchical modeling network structure and its causal mapping mechanism to construct a system transferability index, which serves as a measure of the inherent structural stability of the urban system. The assessment includes the following steps:

[0114] Using the original structure of the urban system hierarchical coupling contribution modeling network model after freezing parameters, the simulation of each type of subsystem (including water resources subsystem, socio-economic subsystem or ecological environment subsystem) in the input sample is carried out in turn. That is, all input indicators under this type of subsystem are replaced with missing states to construct pseudo input samples; at the same time, the original inputs of the other two subsystems are kept unchanged.

[0115] Then, the modified input samples are re-inputted into the trained urban system hierarchical coupling contribution modeling network model to obtain the predicted output, and the deviation Δk between the predicted output and the complete input predicted value is calculated (representing the prediction deviation of the k-th subsystem masked, and k∈[1,3]). Then, Δk is used to... k The reciprocal of the ratio to the original predicted output is used as the transferability index TLk of the k-th subsystem. This index reflects whether other subsystems can compensate for the impact on the overall coordinated development of the city when a certain type of subsystem fails. k ∈[0,1],TL k The larger the value, the higher the system stability and risk response capability. Ultimately, the transferability index TL of the three subsystems will be... k The average value is used to obtain the overall urban development stability (TL) assessment.

[0116] Ultimately, the output of the urban coordinated development inversion assessment module is as follows: System Strategy Inversion Assessment Index (SSI, representing urban development potential), System Coordination Assessment Index (CoD, reflecting the coordination of urban development), and Urban Development Stability Assessment Index (TL, reflecting the stability of current urban development).

[0117] IV. Recommendations for Coordinated Development Paths and Predicted Outcomes

[0118] To achieve structural coordination and full release of development potential among urban water resources, socio-economic factors, and ecological environment, this invention designs a coordinated development path recommendation and effectiveness prediction module. This module is based on the system-level contribution result V obtained by S2. sl Marginal contribution map V ec Using the coupling strength matrix GT as structural prior information, and the evaluation results of S3, a game theory reasoning framework is constructed to achieve multi-round interpretable path deduction and control strategy output. The flowchart of this module is as follows: Figure 3 As shown.

[0119] Collaborative graph construction and variable selection: First, the current state z0 of the city (including all input index values ​​of the three types of subsystems) is defined as the initial state, and combined with the marginal contribution graph V ec The Top-K strategy is used to select K input indicators with the greatest contribution, and a set of control variables, Set, is obtained. conSecondly, the indicators in the set of control variables are used as nodes, and the coupling degree between any two indicators in the coupling strength matrix GT is multiplied by the contribution degree V of the system to which that indicator belongs. sl As edge features, the initial collaborative graph is obtained; where nodes represent control variables and edges represent the overall coupling strength.

[0120] Multi-party game modeling: Three types of urban subsystems are treated as independent game participants, namely: A1, A2, and A3; each subsystem is represented by a set of control variables. con The system selects a subset of its own associated regulatory variables as the strategy space, namely Set1, Set2, and Set3; and constructs the game cost function Loss as the sum of the mean square errors between the current system strategy inversion index assessment SSI, system coordination degree assessment CoD, and urban development stability assessment TL and the three assessments corresponding to the game deduction generation path, thereby ensuring that while achieving the goal of urban coordination, it actively avoids strategies with disadvantageous potential.

[0121] Interpretable path reasoning and optimization guided by cooperative graph: Based on the adjacency matrix and edge weight information of the cooperative graph structure, the indicators in the control variable set are sorted by graph structure through the path with the maximum coupling degree, thereby determining the perturbation priority sequence Seris;

[0122] Subsequently, in each round of game iteration, Seris prioritizes key variables to regulate z0 according to the priority sequence, generating regulation scheme z1. The quality of the generated regulation scheme z1 is then evaluated using the game cost function Loss of S4-2. A graph-guided game update mechanism is employed to update the adjustment order and magnitude of strategies among variables. By minimizing the game cost function Loss, the regulation strategy is continuously updated until iterative convergence to an approximate Nash equilibrium point, ultimately generating the optimal regulation path z. best This refers to the coordinated urban development path that meets the overall system's regulatory objectives.

[0123] Prediction of the effectiveness of the control path: predicting the optimal control path z best The original state z0 is superimposed on the urban system hierarchical coupling contribution modeling network model with frozen parameters, thereby outputting the prediction results of the effectiveness of urban coordinated development indicators.

[0124] V. Experimental Results and Analysis

[0125] To verify the effectiveness of the proposed "Urban Coordinated Development Assessment Method Based on the Coupling of the Water Resources-Socio-Economic-Ecological Environment Tripartite System", this paper conducts experiments using multi-source statistical and remote sensing data from a typical regional city over a five-year development cycle. The objectives are to evaluate the performance of this method in predicting coordinated development status, identifying development deviations, and generating control paths, and to verify its adaptability and interpretability in scenarios of intelligent assessment of urban governance and development strategy deduction.

[0126] 1. Display of Prediction Results for Coordinated Development Status

[0127] This embodiment selects two typical coordinated development indicators: the green development index and the urban sustainable development capacity index, as modeling targets, and uses the constructed urban system hierarchical coupling contribution modeling network model to carry out prediction experiments. Figure 4 and Figure 5 The model output results are shown in comparison with the trajectory of the reference values.

[0128] from Figure 4 It is evident that the proposed model accurately depicts the evolution trend of the green development index, especially in the years with intensive green policy implementation (years 3 and 5), demonstrating a good response to changes and validating the advantages of the model's attention module in handling environmental variables. Figure 5 In this study, the predicted trajectory of the urban sustainable development capacity index closely follows the measured reference value, and the model can accurately capture the potential driving effect of long-term variables such as industrial transformation and infrastructure investment on urban development capacity. Overall results show that the method of this invention can stably model the dynamic changes of urban coordinated development indicators, providing reliable predictive support for subsequent inversion analysis and path recommendation.

[0129] 2. Deviation Analysis of Urban Development Status

[0130] To further verify the ability to identify and explain anomalies in development status, this embodiment uses real-time urban development data as input and identifies key deviation stages through the constructed "system coordination assessment" and "urban development stability assessment" mechanisms. Figure 6 It demonstrates the mutually beneficial and consistent evolutionary trend among the three systems (i.e., water resources, socio-economic, and ecological environment) over the past five years. Figure 7 The evolutionary stability response under different system failure conditions is demonstrated.

[0131] like Figure 6 As shown, the mutual consistency between the socio-economic system and the ecological environment system declined significantly in the third year, indicating that the environmental carrying capacity failed to keep pace with the economic growth rate during the urban development process. Figure 7Furthermore, it is pointed out that when the input of the ecological environment subsystem is missing, the deviation in the predicted output of coordinated urban development is the greatest, and the stability index drops below 0.72, indicating that it plays a key supporting role in the urban system. Based on the system strategy inversion index assessment, it can be determined that the current development status has the risk of "environmental bottleneck deviation". This result verifies the ability of this invention in structural deviation explanation and causal diagnosis.

[0132] 3. Recommended Development Regulation Path

[0133] Based on the deviation analysis results of the second stage, the proposed coordinated development path recommendation mechanism is used to construct a collaborative graph and conduct multi-round game reasoning to output the regulation path and predict the effect. Figure 8 Display the perturbation sequence of the regulatory variables and their priority ranking. Figure 9 This is a comparison of the predicted output indicators of the model under the original and controlled conditions.

[0134] The results show that, under the premise of maintaining the stability of urban economic growth targets, the system recommends prioritizing the adjustment of the following variables: increasing the sewage treatment rate by 7.2%, increasing the green coverage rate of built-up areas to 43%, and optimizing the per capita water use structure. Figure 9 The results show that after applying the control path, both the green development index and the urban sustainable development capacity index have significantly improved and are approaching the target range, verifying the accuracy of the strategy generation mechanism in terms of control priority ranking and scheme feasibility.

[0135] Therefore, the urban coordinated development assessment method proposed in this invention can not only accurately model key indicators, but also has the ability to identify development deviations, analyze structural sources, and generate control paths, making it suitable for intelligent decision-making and dynamic management tasks in diverse urban development scenarios.

[0136] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

[0137] While the specific embodiments of the present invention have been described above, they are not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for assessing coordinated urban development based on water resources and their coupling factors, characterized in that, Includes the following processes: S1: Collect structural characteristic indicators of three subsystems covering the target urban area: water resources, socio-economic and ecological environment, and construct a structured dataset for modeling coordinated urban development; extract representative indicators from the subsystems as input features, and use coordinated development labels composed of quantifiable physical indicators as output; S2, construct the hierarchical coupling contribution modeling network of urban system, including the system-level influence analysis network and the index-level coupling modeling network, the former captures the heterogeneous semantic relationship between subsystems and generates system-level feature representation F Ss ; the latter constructs the original graph structure data based on the input index data, extracts the node interaction representation, and fuses to generate the index-level coupling contribution feature F Sm ; based on the first-level output F Ss and the second-level output F Sm , the prediction result of the urban coordinated development index is obtained; the data set collected by S1 is used for model training; S3. After the model is trained, its structural interpretability is used to conduct a multi-dimensional inversion assessment of the city's coordinated development status: based on the expected coordinated development indicators, the minimum indicator disturbance cost required to achieve the target development status is calculated through the strategy inversion mechanism, forming the system strategy inversion assessment index SSI; based on the training model and the response behavior of its internal subsystems, simulation regulation and consistency inference are carried out to output the system coordination degree assessment index CoD. Based on the training model structure and its causal mapping mechanism, a system transferability index is constructed to obtain the urban development stability assessment index TL.

2. The urban coordinated development assessment method based on water resources and its coupling factors as described in claim 1, characterized in that: It also includes the following processes: Based on the urban system hierarchical coupling contribution modeling network model obtained by S2, the global influence contribution between the network modeling systems is analyzed based on the first-level system, and the marginal influence and cross-coupling relationship of the input index of the network modeling are modeled based on the second-level index, to obtain the system-level influence index result V reflecting the contribution degree of the system-level data sl , the index marginal contribution atlas V reflecting the contribution degree of the index-level data ec , and the coupling strength matrix GT reflecting the coupling degree of the index-level data Based on the output evaluation results, a game reasoning framework is constructed to recommend multi-round urban coordinated development regulation paths; water resources, socio-economic and ecological environment systems are treated as independent game subjects, and a game cost function is constructed with three-dimensional evaluation indicators; a graph-guided game mechanism is used to iteratively generate perturbation sequences and seek optimization, and finally output an interpretable coordinated development regulation path.

3. The urban coordinated development assessment method based on water resources and its coupling factors as described in claim 1, characterized in that: The water resource subsystem index WS includes: water resource per capita WS pc , water production modulus WS pm , groundwater supply proportion WS gs , industrial water proportion WS pi , agricultural irrigation water amount WS ai , water resource development and utilization rate WS du , water resource utilization efficiency WS ue , annual average precipitation WS ap ; Socio-economic subsystem indicators include SE includes: GDP per capita SE pc , the first / second / third industry proportion SE fp , SE sp , SE tp , total fixed asset investment SE tf , population density SE pd , urbanization rate SE ur , total retail sales of social consumer goods SE tr , public financial expenditure proportion SE fe ; The ecological environment subsystem index EE includes: built-up area green coverage rate EE gu , solid waste comprehensive utilization rate EE sw , wastewater discharge per ten thousand yuan of GDP EE wd , carbon emission per unit area EE ce , sewage treatment rate EE st , air quality standard days EE eq , ecological red line proportion EE rl .

4. The urban coordinated development assessment method based on water resources and its coupling factors as described in claim 1, characterized in that: The quantifiable physical index label includes resource-environment carrying strength index DV rc , green development index DV gd , regional coordinated development index DV ac , and urban sustainable development capacity index DV cs .

5. The urban coordinated development assessment method based on water resources and its coupling factors as described in claim 1, characterized in that: The specific urban system hierarchical coupling contribution modeling network model is as follows: The primary system level influence analysis network, three types of subsystem index data are respectively converted through two fully connected layers, and layer standardization and ReLU activation function are used to improve the feature nonlinear expression ability; then the model generalization ability is enhanced through the Dropout layer; the converted three types of feature vectors are fused through the multi-dimensional heterogeneous perception attention layer to capture the heterogeneous semantic relationship between the subsystems and generate the system level feature representation, denoted as system structure feature F Ss ; The secondary index level coupling modeling network first directly takes all index data as input without division; then each index is represented as a node, and edges are constructed for possible coupling relationships according to prior knowledge, to obtain original graph structure data; then a two-layer graph attention network layer is used to extract node interaction representation, and the graph structure feature F is recorded Gs ; then two branches are entered: The marginal contribution modeling branch: F Gs The input multi-layer perception, and then enter the conditional attribution attention layer to capture the marginal importance of different indicators, and output the indicator marginal influence representation F Me ; The interaction coupling modeling branch: F Gs After inputting the multi-layer perception, multi-order interaction modeling is performed through the CrossNet cross feature coding layer, and coupled interaction features F Ci ; The two-branch outputs are dynamically fused through a gating fusion mechanism to generate index-level coupled contribution features F Sm ; Finally, the first-level output F Ss is combined with the second-level output F Sm through a fully connected layer, and is mapped to a coordinated development label space through a ReLU activation function to obtain a prediction result DV of the final urban coordinated development index. pre .

6. The urban coordinated development assessment method based on water resources and its coupling factors as described in claim 1, characterized in that: The specific process for obtaining the System Strategy Inversion Evaluation Index (SSI) is as follows: First, set a set of expected urban coordinated development indicators (DV). best Use the trained model and freeze the model parameters and structure; Secondly, the three subsystem indicators WS, SE and EE are concatenated as the complete input data Cod, which is used as the initial data x0. The controllable indicator variables are selected as optimization variables to generate multiple control data x′. The optimization objective is set as minimizing the sum of the control achievable loss and the control cost; where the control achievable loss is the sum of the urban coordinated development forecast result obtained with control data x′ as input and the DV. best The mean square error between the control data x′ and the initial data x0 is taken as the control cost, which is the L1 norm between the control data x′ and the initial data x0. With this as the objective, the L-BFGS optimizer is selected to search for the minimum perturbation input vector x that satisfies the target output. * ; Then, calculate x * The L2 norm, which differs from x0, serves as the strategic intervention cost for adjusting the city's state, i.e., the system strategy inversion evaluation index (SSI).

7. The urban coordinated development assessment method based on water resources and its coupling factors as described in claim 1, characterized in that: The specific process for obtaining the system coordination degree evaluation index CoD is as follows: For the first-level system-level influence analysis network of the trained model, firstly, the response features FS1, FS2, and FS3 of the first three systems entering the multidimensional heterogeneous perception attention layer are recorded when the complete input data Cod is used as input. Then, a small perturbation is applied to the input index of any one of the three systems, while the inputs of the other two systems remain unchanged. The training model is then run once to obtain the response features FS1, FS2, and FS3 after adjusting the input. Finally, the partial derivative between the response of the p-th fixed subsystem and the q-th perturbation subsystem is calculated to obtain the cross-system influence mapping tensor R. q→p And p,q∈[1,3]; Extensive testing was conducted on each subsystem, and the results were averaged to obtain the complete cross-system impact mapping matrix R; subsequently, the reciprocity consistency r was calculated. qp The mutual consistency calculation results r between each pair of the three systems are obtained. 12 r 13 r 23 Finally, the average of the three is taken as the system coordination degree CoD evaluation result, and CoD∈[0,1].

8. The urban coordinated development assessment method based on water resources and its coupling factors as described in claim 1, characterized in that: The specific process for obtaining the urban development stability assessment index TL is as follows: Using the original structure of the S2 model after freezing parameters, masking simulation is performed on each subsystem in the input sample in turn, that is, all input indicators under the subsystem are replaced with missing states to construct pseudo-input samples; at the same time, the original inputs of the other two subsystems are kept unchanged. Then, the modified input samples are re-inputted into the trained model to obtain the predicted output, and the deviation Δ between the predicted output and the full input predicted value is calculated. k Then use Δ k The reciprocal of the ratio to the original predicted output is used as the transferability index TL of the k-th subsystem. k This indicator reflects whether other subsystems can compensate for the failure of a certain type of subsystem in order to improve the overall coordinated development of the city, and TL k ∈[0,1],TL k The larger the value, the higher the system stability and risk response capability. Ultimately, the transferability index TL of the three subsystems will be... k The average value is used to obtain the city's overall development stability assessment index TL.

9. The urban coordinated development assessment method based on water resources and its coupling factors as described in claim 2, characterized in that, The system-level impact index result V sl The acquisition process is as follows: For the first-level system-level impact analysis network, a system-level contribution structure mapping process is constructed: First, the attention weight tensors of three types of subsystems are extracted from the multi-dimensional heterogeneous perception attention layer, and then normalized to form the subsystem structure contribution vector V. sc This vector reflects the degree of global impact of different subsystems on the prediction of coordinated urban development under multiple rounds of attention. Secondly, a distributed response mapping mechanism is introduced: after subjecting the original subsystem input to a uniform amplitude incremental perturbation, a new output result is obtained through model inference, and the relative change rate of the model output relative to the original output is defined as the system perturbation response intensity V. sd ; Finally, using the system disturbance response strength V sd This represents the overall robustness of the model against interference, multiplied by a preset interference weight α. sd Added to the system structure contribution vector V sc In the process, the system-level impact index result V was obtained. sl .

10. The urban coordinated development assessment method based on water resources and its coupling factors as described in claim 2, characterized in that, The marginal contribution map V of the indicator ec The process of obtaining the coupling strength matrix GT is as follows: We analyze the second-level indicator-level coupled modeling network and construct an indicator-level parsing framework with two dimensions: marginality and interaction. Marginal contribution modeling path: Extract the trained normalized attention weight vector V from the output of the marginal contribution modeling branch of the second-level modeling network. wn This directly reflects the strength of the model's response to different input indicators; Simultaneously, combining the nonnegativity and sparsity regularization terms introduced in the model structure, V wn Perform structural attribution deconstruction to generate an indicator marginal contribution map V. ec ; Interactive coupling modeling path: Extracting cross-feature vectors from the CrossNet layer output based on the interactive modeling branch in the second-level network. This represents the cross-feature vector between the i-th and j-th indicators; After that, Calculate the L2 norm to obtain the joint feature expression strength between the two indicators. The larger the value, the stronger the interactivity, and this value is used as the indicator coupling strength. By quantifying the cross-coupling strength of each pair of indicators in model inference, the complete coupling strength matrix GT between indicator pairs is finally constructed.

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