A human-oriented analysis and optimization method for disaster resilience improvement of water supply network

Abstract

The application discloses a human-oriented analysis and optimization method for disaster resilience improvement of a water supply network, and aims at overcoming the shortage that the existing water supply network disaster resilience research takes engineering water supply indexes as the only optimization target and ignores population suffering dynamics. The application discloses a human-oriented analysis and optimization method for disaster resilience improvement of a water supply network, and aims at overcoming the shortage that the existing water supply network disaster resilience research takes engineering water supply indexes as the only optimization target and ignores population suffering dynamics. The application discloses a human-oriented analysis and optimization method for disaster resilience improvement of a water supply network, and aims at overcoming the shortage that the existing water supply network disaster resilience research takes engineering water supply indexes as the only optimization target and ignores population suffering dynamics. The application discloses a human-oriented analysis and optimization method for disaster resilience improvement of a water supply network, and aims at overcoming the shortage that the existing water supply network disaster resilience research takes engineering water supply indexes as the only optimization target and ignores population suffering dynamics. The application discloses a human-oriented analysis and optimization method for disaster resilience improvement of a water supply network, and aims at overcoming the shortage that the existing water supply network disaster resilience research takes engineering water supply indexes as the only optimization target and ignores population suffering dynamics.

Description

Technical Field

[0001] This invention belongs to the field of disaster prevention and mitigation in urban lifeline engineering. Specifically, it relates to a humanistic analysis and optimization method that combines engineering physical simulation with population welfare quantification and is geared towards improving the disaster resilience of water supply networks (WDS). It is applicable to population suffering assessment, proxy-assisted multi-objective optimization, and reinforcement strategy decision-making in the entire process of post-disaster damage and recovery of urban water supply networks. Background Technology

[0002] Urban water supply networks are a critical lifeline system supporting the normal operation of cities. Damage to these networks during disasters can lead to water outages, resulting in suffering for days or even weeks. In recent years, research on infrastructure resilience has increasingly recognized that the core impact of disasters is human suffering rather than simply engineering damage. Scholars have divided population well-being measurement into two dimensions: objective well-being (deprivation of daily activities, loss of capacity) and subjective well-being (experience of suffering, negative emotions), and have established several quantitative models. However, existing models are mostly designed for general infrastructure disruptions and lack adaptation to the pressure-related demand mechanisms specific to water supply networks.

[0003] In the area of ​​disaster resilience analysis for water supply networks, existing research has established an engineering workflow centered on disaster hazard characterization, pipeline damage models, post-disaster hydraulic analysis, recovery simulation, and optimization. Specifically, ground motion prediction equations and spatial correlation models are jointly used to generate probabilistic hazard fields; vulnerability functions are used to estimate pipeline damage; pressure-related demand and explicit leakage models characterize service degradation; recovery simulation with repair team constraints generates service recovery trajectories; and machine learning surrogate models significantly reduce computational overhead. However, almost all of these advances use engineering indicators (such as the Water Insufficiency Index (SDI), System Serviceability Index, and Connectivity Indicators) as objective functions, failing to directly link physical system recovery with population well-being outcomes.

[0004] Existing methods for analyzing the disaster resilience of water supply networks suffer from three main shortcomings: First, they lack a comprehensive resilience enhancement framework that integrates hazard assessment, damage uncertainty, hydraulic analysis, recovery simulation, and efficient, human-centered decision-making optimization. Second, engineering water supply indicators such as SDI (Solar Distress Indicators) cannot characterize activity-based tolerance levels or the cumulative suffering under prolonged interruptions. Third, there is a lack of comparative evidence between hardship reduction-oriented and SDI-oriented reinforcement decisions, making it difficult to guide planners in determining when and why investments should be reallocated with a welfare-oriented objective. Therefore, a human-centered disaster resilience enhancement method that links the physical interruption recovery mechanism of water supply networks with the welfare consequences for the population is urgently needed. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of existing research on the disaster resilience of water supply networks, which takes engineering water supply indicators as the sole optimization target and ignores the dynamics of human suffering. Instead, it provides a humanistic analysis and optimization method for improving the disaster resilience of water supply networks.

[0006] The human-centered analysis and optimization method for improving the disaster resilience of water supply networks, as described in this invention, is implemented according to the following steps:

[0007] Step 1: Disaster Risk Characterization and Pipeline Damage Scenario Generation

[0008] Using the moment magnitude Mw, focal location, and focal depth of the scenario earthquake disaster as input, the median predicted peak ground velocity (PGV) of each water supply network node in the target area is calculated using the Ground Motion Prediction Equation (GMM); the logarithm of the median predicted value is then taken to obtain the logarithmic PGV.

[0009] The total uncertainty of logarithmic PGV is decomposed into inter-event residuals. (All nodes share a single sample value under the same disaster event) Spatially correlated intra-field residuals Two parts, thus constructing N spatially related ground sports fields;

[0010] For each spatially related ground sports field, the water supply pipeline is calculated according to the power-law corrected restoration rate formula. Repair rate per unit length Thus, a water supply pipeline was obtained. Probability of damage ;

[0011] The formula for the power-law correction rate is as follows:

[0012]

[0013] In the formula As the baseline repair rate, The reference peak ground velocity corresponding to the baseline repair rate. For water supply pipes peak ground speed, This is the intensity scaling index. For material correction factors, This is the pipe diameter correction factor. For terrain correction factors, This is a liquefaction multiplicative correction factor;

[0014] water supply pipes Probability of damage Based on conditional probability calculations, the water supply pipelines were obtained respectively. The probability of fracture and the probability of leakage are combined with Monte Carlo sampling to construct a large-scale pipeline damage scenario (library).

[0015] Step Two: Post-Disaster Hydraulic Analysis and Quantification of Human Suffering

[0016] For each pipeline damage scenario, the water supply pipeline is divided into three states: intact, broken, and leaking. The broken pipeline is isolated from the water supply network, and a virtual leak node is introduced for the leaking pipeline and the leakage flow is simulated to obtain the daily water supply of each node in the water supply network.

[0017] Divide the daily water supply of a node by the population it serves to obtain the average daily water consumption per person. Greedily allocate the average daily water consumption per person according to different water-related daily activities. When the water consumption for a certain water-related daily activity is less than the minimum water demand, the deprivation time is accumulated daily. Then, a bounded sigmoid suffering degree function is used to map the accumulated deprivation time to the instantaneous suffering of the corresponding water-related daily activity. The instantaneous suffering at the node level is the sum of the instantaneous suffering of all water-related daily activities. The system-level instantaneous suffering is obtained by weighting all node-level instantaneous sufferings with the population served by the node as the weight. The system-level instantaneous suffering is obtained by summing the system-level instantaneous sufferings daily over the T-day recovery period.

[0018] Step 3: Agent Model Construction and Multi-Objective Optimization

[0019] The input feature is formed by splicing the three-state unique hot coding of the water supply pipeline with the global damage count. The global damage count is the total number of broken water supply pipelines and the total number of leaking water supply pipelines in the water supply network within the target area. The cumulative suffering ΣT* is the output feature. The cumulative suffering feedforward artificial neural network (ANN) surrogate model is trained to obtain the trained cumulative suffering surrogate model.

[0020] Step 4: Output of Human-Centered Resilience Enhancement Strategies:

[0021] Based on the trained cumulative suffering surrogate model, the binary decision vector is used to determine whether to reinforce the water supply pipeline. The dual objectives are the total reinforcement cost and the cumulative suffering predicted by the trained cumulative suffering surrogate model. The Pareto optimization is performed using the NSGA-II multi-objective evolutionary algorithm to output a set of reinforcement strategies that minimize cumulative suffering under different total reinforcement cost constraints. This completes a human-centered analysis and optimization method for improving the disaster resilience of water supply networks.

[0022] The human-centered analysis and optimization method for improving the disaster resilience of water supply networks, as described in this invention, has the following beneficial effects:

[0023] First, the proposed human-centered resilience enhancement framework couples hydraulic mechanisms, water-related daily activity patterns, and the dynamic system of population suffering, shifting the assessment focus from engineering supply performance to public well-being.

[0024] Second, the proposed bounded sigmoid suffering degree function (SLF) quantitatively characterizes population suffering through a triple mechanism of activity deprivation dynamics, tolerance level exceeding, and saturation upper limit, avoiding the numerical divergence of the exponential function under long-term water outages, while retaining the rapid escalation characteristic of suffering near the tolerance threshold.

[0025] Third, the proposed agent-assisted multi-objective optimization method reduces the computational cost of evaluating millions of scenarios from hours to milliseconds, supporting real-time optimization decisions for large-scale pipeline networks.

[0026] Fourth, the human-centered optimization strategy prioritizes reinforcing medium-diameter water distribution pipelines that directly supply water to vulnerable populations. Compared to the SDI-driven large-diameter trunk pipeline optimization strategy, this approach can cover a higher proportion of the total population and achieve a greater reduction in water outage duration for high-risk groups. Attached Figure Description

[0027] Figure 1 This is a comparison chart of the bounded Sigmoid suffering function and the Yang exponential function within the tolerance range (normalized scale) in the embodiment.

[0028] Figure 2 This is a comparison chart of the bounded Sigmoid hardship function, the Yang exponential function (logarithmic scale), and the upper limit of saturation in the embodiment.

[0029] Figure 3 This is a diagram showing the water supply network topology, node demand distribution, and pipeline characteristics in the example.

[0030] Figure 4 This is a spatial distribution map of representative damage scenarios (28 pipeline damages: 6 fractures and 22 leaks) under the median disaster intensity in the example.

[0031] Figure 5 The figure shows the evolution curve of the system-level average cumulative distress under the PNF-PCI repair strategy for representative damage scenarios in the examples.

[0032] Figure 6 This is a graph showing the evolution of the node-level average cumulative suffering and daily water supply for representative demand nodes in a representative damage scenario in the embodiment.

[0033] Figure 7 The SDI-AUC surrogate model verification diagram in the example (comparison of predicted values ​​and true values ​​in the full-process simulation).

[0034] Figure 8 This is a verification diagram of the cumulative suffering proxy model in the example (comparison of predicted values ​​and true values ​​in the full-process simulation).

[0035] Figure 9 This is a comparison chart showing the evolution of accumulated suffering with the number of days of post-disaster recovery under different enhancement strategies in the embodiments;

[0036] Figure 10 This is a comparison chart of the water outage durations of the optimal SDI and optimal SLF strategies from the perspective of risk stratification in the embodiments.

[0037] Figure 11 This is a comparison chart of the reduction efficiency of the optimal SDI and optimal SLF strategies from the perspective of risk stratification in the embodiments. Detailed Implementation

[0038] Specific Implementation Method 1: This implementation method, which focuses on the human-centered analysis and optimization approach to improve the disaster resilience of water supply networks, is carried out according to the following steps:

[0039] Step 1: Disaster Risk Characterization and Pipeline Damage Scenario Generation

[0040] Using the moment magnitude Mw, focal location, and focal depth of the scenario earthquake disaster as input, the median predicted peak ground velocity (PGV) of each water supply network node in the target area is calculated using the Ground Motion Prediction Equation (GMM); the logarithm of the median predicted value is then taken to obtain the logarithmic PGV.

[0041] The total uncertainty of logarithmic PGV is decomposed into inter-event residuals. (All nodes share a single sample value under the same disaster event) Spatially correlated intra-field residuals Two parts, thus constructing N spatially related ground sports fields;

[0042] For each spatially related ground sports field, the water supply pipeline is calculated according to the power-law corrected restoration rate formula. Repair rate per unit length Thus, a water supply pipeline was obtained. Probability of damage ;

[0043] The formula for the power-law correction rate is as follows:

[0044]

[0045] In the formula As the baseline repair rate, The reference peak ground velocity corresponding to the baseline repair rate. For water supply pipes peak ground speed, This is the intensity scaling index. For material correction factors, This is the pipe diameter correction factor. For terrain correction factors, This is a liquefaction multiplicative correction factor;

[0046] water supply pipes Probability of damage Based on conditional probability calculations, the water supply pipelines were obtained respectively. The probability of fracture and the probability of leakage are combined with Monte Carlo sampling to construct a large-scale pipeline damage scenario (library).

[0047] Step Two: Post-Disaster Hydraulic Analysis and Quantification of Human Suffering

[0048] For each pipeline damage scenario, the water supply pipeline is divided into three states: intact, broken, and leaking. The broken pipeline is isolated from the water supply network, and a virtual leak node is introduced for the leaking pipeline and the leakage flow is simulated to obtain the daily water supply of each node in the water supply network.

[0049] Divide the daily water supply of a node by the population it serves to obtain the average daily water consumption per person. Greedily allocate the average daily water consumption per person according to different water-related daily activities. When the water consumption for a certain water-related daily activity is less than the minimum water demand, the deprivation time is accumulated daily. Then, a bounded sigmoid suffering degree function is used to map the accumulated deprivation time to the instantaneous suffering of the corresponding water-related daily activity. The instantaneous suffering at the node level is the sum of the instantaneous suffering of all water-related daily activities. The system-level instantaneous suffering is obtained by weighting all node-level instantaneous sufferings with the population served by the node as the weight. The system-level instantaneous suffering is obtained by summing the system-level instantaneous sufferings daily over the T-day recovery period.

[0050] Step 3: Agent Model Construction and Multi-Objective Optimization

[0051] The input feature is formed by splicing the three-state unique hot coding of the water supply pipeline with the global damage count. The global damage count is the total number of broken water supply pipelines and the total number of leaking water supply pipelines in the water supply network within the target area. The cumulative suffering ΣT* is used as the output feature to train the cumulative suffering feedforward artificial neural network (ANN) surrogate model, and the trained cumulative suffering surrogate model is obtained.

[0052] Step 4: Output of Human-Centered Resilience Enhancement Strategies:

[0053] Based on the trained cumulative suffering surrogate model, the binary decision vector is used to determine whether to reinforce the water supply pipeline. The dual objectives are the total reinforcement cost and the cumulative suffering predicted by the trained cumulative suffering surrogate model. The Pareto optimization is performed using the NSGA-II multi-objective evolutionary algorithm to output a set of reinforcement strategies that minimize cumulative suffering under different total reinforcement cost constraints. This completes a human-centered analysis and optimization method for improving the disaster resilience of water supply networks.

[0054] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that the expression for the logarithm PGV of the water supply network nodes in step one is as follows:

[0055]

[0056] in, This is the midpoint prediction function in the ground motion prediction equation. For the first Joyner-Boore distance of the node For site and path parameter vectors, For the inter-event residuals, This represents the spatially correlated field residuals.

[0057] In this embodiment, Y i Let Y be the peak ground velocity (PGV) at node i (in cm / s). i That is, the logarithm PGV; μ PGV M is the median prediction function given by the ground motion prediction equations calibrated in the region; w The moment magnitude of the scenario-based disaster; R JB,i η is the shortest horizontal distance (in km) from node i to the rupture surface of the earthquake source in the Joyner-Boore region. i The site and path parameter vector at node i includes at least the site shear wave velocity index VS30 (average shear wave velocity of soil layers within a depth of 30 m below the surface), fault type indicator, and basin depth parameter. For the residuals between events, a single sampled value is shared by all nodes under the same disaster event; Let be the spatially correlated field residual of node i.

[0058] In this implementation method, the residual vector within the field... Modeled as an isotropic correlation function

[0059]

[0060] A Gaussian process with covariance kernel, where For nodes With nodes Spatial distance, For the relevant length, For shape parameters.

[0061] Specific Implementation Method Three: This implementation method differs from Specific Implementation Method One or Two in that the water supply pipeline in step one... Probability of damage The calculation formula is:

[0062]

[0063] in For the length of the pipe, For water supply pipes Repair rate per unit length.

[0064] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One to Three in that, in step two, a virtual leakage node is introduced into the leaking pipeline and the leakage flow rate is simulated. The simulated leakage flow rate is determined by the thin orifice equation.

[0065]

[0066] in The orifice coefficient, The desired leakage area (parameterized by pipe diameter, joint density, and material). It is the acceleration due to gravity. This refers to a localized water head.

[0067] In this embodiment, when the node head... Below the minimum service head When the water supply is zero, Higher than the design service head Hourly water supply equals nominal demand Intermediate states are determined by a power function:

[0068]

[0069] Perform interpolation.

[0070] Specific Implementation Method Five: This implementation method differs from Specific Implementation Methods One to Four in that the daily water-related activities in step two are divided into five categories: drinking water, cooking, using the toilet, bathing, and washing.

[0071] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One through Five in that step two includes a bounded Sigmoid difficulty function. The expression is:

[0072]

[0073] in The upper limit of saturation, The steepness parameter controls the rate of increase of instantaneous suffering near the inflection point; a larger value indicates that the suffering escalates rapidly as the duration of deprivation extends. For water-related activities Cumulative deprivation time (days) since the last successful completion. It represents the inflection point of the bounded sigmoid function for the degree of suffering.

[0074] In this embodiment, the instantaneous hardship of the activity is represented by the daily water-wading activity a at node i. The instantaneous suffering of a day is dimensionless; the larger the value, the greater the instantaneous pressure that the activity's deprivation of people's well-being causes.

[0075] In this embodiment , For daily water-related activities At the node The random tolerance level reflects the heterogeneity of the population's tolerance to the deprivation of the activity. Δ is the inflection point offset (in days), defined as the typical buffer time required to reach the vicinity of the saturation upper limit after the tolerance level is exceeded. It is obtained by minimizing the root mean square deviation between the Yang exponential model and the sigmoid function near the tolerance threshold.

[0076] Specific Implementation Method Seven: This implementation method differs from Specific Implementation Method Six in that when the daily water-related activity is drinking water... ρ is the shape parameter of the Yang exponential model, and TL drink Tolerance level for drinking water activities.

[0077] The tolerance levels for other water-related activities in this embodiment are shown in Table 3 below.

[0078] Specific Implementation Method Eight: This implementation method differs from Specific Implementation Methods One through Seven in that the system-level instantaneous suffering in step two is... The expression is:

[0079]

[0080] in For water supply network nodes The service population, Let A be the set of all demand nodes, and let A represent different daily water-related activities.

[0081] Specific Implementation Method Nine: This implementation method differs from Specific Implementation Methods One to Eight in that the cumulative suffering feedforward artificial neural network (ANN) surrogate model in step three consists of an input layer, two hidden layers, and an output layer. The number of neurons in the first hidden layer is 128, and the number of neurons in the second hidden layer is 64. The ReLU activation function is used.

[0082] Specific Implementation Method Ten: This implementation method differs from Specific Implementation Methods One through Nine in that step four uses whether or not reinforcement is implemented on each pipeline as a binary decision vector, and takes the total reinforcement cost of the water supply pipeline and the predicted cumulative hardness as dual objectives. The expression for the total reinforcement cost is as follows:

[0083]

[0084] in =1 indicates that pipe k is selected as the reinforcement target. The unit price for reinforcement of pipe k per unit length (yuan / km, determined by the regional municipal cost manual according to pipe diameter classification). Let N be the length of pipe k. p This represents the total number of pipelines in the network.

[0085] Example: This example takes the water supply network of a certain city as the object, and implements a human-centered analysis and optimization method for improving the disaster resilience of the water supply network according to the following steps:

[0086] Step 1: Disaster Risk Characterization and Pipeline Damage Scenario Generation

[0087] This embodiment describes a water supply network serving a densely populated urban area, such as... Figure 3 As shown, the system consists of 68 water supply network nodes and 92 pipelines, supplied by a reservoir with a head of 45 m. The pipeline diameters range from 400 to 1200 mm, and the material composition is: 45% ductile iron, 31% gray cast iron, 20% asbestos cement, and 4% steel. It serves a total population of 8.67 million, with node demand ranging from 12 to 185 L / s and a total system demand of 3847 L / s. Hydraulic parameters include a Hazen-Williams roughness coefficient of 100–130 and a minimum service head of [missing information]. m, design service water head m, Pressure-Demand Index Leakage orifice coefficient In its optimal state, the system meets all requirements, with a minimum node pressure of 22.3 m. Twelve nodes (including the hospital, emergency center, and high-density residential area) have been designated as priority nodes.

[0088] Using the intensity parameter Mw of the scenario disaster, the location of the epicenter, and the focal depth as inputs, the median predicted value of the peak ground velocity (PGV) at each water supply network node is calculated using the regionally calibrated Ground Motion Prediction Equation (GMM). The logarithmic value of the PGV at each node is expressed as follows:

[0089]

[0090] in This is the midpoint prediction function in the ground motion prediction equation. For the first Joyner-Boore distance of the node For site and path parameter vectors, For the inter-event residuals, For spatially correlated field residuals; spatially correlated field residuals The model is based on an isotropic correlation function;

[0091]

[0092] A Gaussian process with covariance kernel, where For nodes and Spatial distance, For the relevant length, For shape parameters.

[0093] The correlation length λcorr characterizes the characteristic scale of the spatial correlation of ground motion residuals between different nodes as the distance decreases—when the distance between two nodes is less than λcorr, their residuals are strongly positively correlated, and when the distance is much greater than λcorr, the residuals are approximately independent; the shape parameter κ controls the decay pattern of the correlation function.

[0094] The relevant length of this embodiment km, Each PGV field underwent 200 conditional damage Monte Carlo sampling iterations, resulting in a total of [number missing] samples. A pipeline damage scenario ( Figure 4 ).

[0095] For each spatially related ground sports field, the water supply pipeline is calculated according to the power-law corrected restoration rate formula. Repair rate per unit length Thus, a water supply pipeline was obtained. Probability of damage ;

[0096] The formula for the power-law correction rate is as follows:

[0097]

[0098] In the formula Baseline repair rate times / km, The normalized intensity reference value is represented by the intensity scaling index. , The material correction factor is 0.3 to 1.2. The pipe diameter correction factor is 0.5 ( From 1.6 (75 mm) to 1.6 (75 mm). For terrain correction factors, This is a liquefaction multiplicative correction factor;

[0099] The sources of the above parameter values ​​are as follows: the baseline repair rate RR0 = 0.32 times / km and the normalized strength reference value PGVref = 50 cm / s (i.e., the expected number of damages per unit length of pipe at PGV = 50 cm / s is 0.32 times / km) are both taken from the calibration values ​​of the American Lifelines Alliance (ALA, 2001) and the vulnerability study of this region; the strength scaling index β = 1.30; the specific values ​​of the pipe material correction factor Cmat,k and the pipe diameter correction factor Cdia,k are given in Tables 1 and 2 below; the terrain correction factor... Take 1.0 (no significant slope in this case area); liquefaction multiplicative correction factor Set the value to 1.0 (there is no liquefaction layer in this case area).

[0100] Then, the water supply pipes are obtained according to conditional probability. The probability of fracture and the probability of leakage, the probability of fracture condition This embodiment contains 28 instances of pipeline damage (6 fractures and 22 leaks), and a large-scale pipeline damage scenario library is constructed by combining Monte Carlo sampling.

[0101] Step Two: Post-Disaster Hydraulic Analysis and Quantification of Human Suffering

[0102] For each pipeline damage scenario, the water supply pipeline is divided into three states: intact, broken, and leaking. The broken pipeline is isolated from the water supply network, and a virtual leak node is introduced for the leaking pipeline to simulate the leakage flow rate. The simulated leakage flow rate is determined by the thin orifice equation.

[0103]

[0104] in The orifice coefficient, The desired leakage area (parameterized by pipe diameter, joint density, and material). It is the acceleration due to gravity. For local water head;

[0105] This allows us to obtain the daily water supply volume (time series) of each node in the water supply network.

[0106] Based on each demand node i daily (step size) Water supply time series (=1 day) (That is, the actual water supply of the node on that day is obtained from the post-disaster hydraulic analysis, and is obtained by combining the thin orifice equation with the pressure-related demand model and using the Newton-Raphson iterative solution to solve the head and flow distribution of all nodes in the network.) Divide by the population served (Pi) to obtain the first The average daily water consumption per person is calculated. Water is greedily allocated in descending order of instantaneous suffering for five water-related daily activities: drinking, cooking, toileting, bathing, and washing. If the water allocated to activity 'a' is not less than its minimum water requirement 'ma' (see Table 3), it is considered successfully completed, and the accumulated deprivation time is reset to zero; otherwise, the accumulated deprivation time is increased by one day from the previous day. Then, a bounded Sigmoid suffering degree function is used to map the accumulated deprivation time to the instantaneous suffering of each water-related activity. Node-level instantaneous suffering is the sum of the instantaneous suffering of the five activity categories. The system-level instantaneous suffering is obtained by weighting the node-level instantaneous suffering of all demand nodes based on the population served by each node. The cumulative suffering ΣT* is obtained by summing the system-level instantaneous suffering daily over the T-day recovery period.

[0107] Where there is a bounded Sigmoid function for the degree of suffering. The expression is:

[0108]

[0109] in The upper limit of saturation, The steepness parameter controls the rate of increase of instantaneous suffering near the inflection point; a larger value indicates that the suffering escalates rapidly as the duration of deprivation extends. For water-related activities Cumulative deprivation time (days) since the last successful completion. For a specific inflection point of a node;

[0110] Step 3: Agent Model Construction and Multi-Objective Optimization

[0111] The input feature is a 3Np+2 dimensional vector concatenated with the three-state "intact / leaking / fractured" encoding of pipelines (each pipeline occupies 3 dimensions, for a total of Np pipelines and 3Np dimensional binary features) and the global damage count (i.e., the total number of leaking pipelines and the total number of fractured pipelines in the entire network, totaling 2 dimensions). This vector is then normalized using z-score. The time integral of the water shortage index SDI during the T-day recovery period, SDI-AUC (i.e., the daily SDI over time, which, when using a daily step size, is the sum of the daily SDIs within T days), is used. The daily SDI (sum of actual water supply across the entire network on that day ÷ sum of nominal demand across the entire network) is used as the output label to train a feedforward artificial neural network (ANN) to obtain the trained SDI-AUC surrogate model. The ANN contains one input layer, two hidden layers, and one output layer. In this embodiment, Np=92, so the input dimension is 3×92+2=278, and the network structure is 278 → 128 → 64 → 1. The first hidden layer has 128 neurons, and the second hidden layer has 64 neurons, both using the ReLU activation function with L2 weight decay. The output layer has one neuron with linear activation, outputting a single real-valued scalar, which is the SDI-AUC value predicted by the surrogate model.

[0112] The input feature is formed by concatenating the three-state one-hot encoding of the water supply pipeline with the global damage count, where the global damage count is the total number of broken water supply pipelines and the total number of leaking water supply pipelines in the target area's water supply network. The cumulative suffering ΣT* is the output feature. The cumulative suffering feedforward artificial neural network (ANN) surrogate model is trained to obtain the trained cumulative suffering surrogate model. The SDI-AUC surrogate model and the cumulative suffering surrogate model use the exact same network topology and training method, only the training labels and final weights are different.

[0113] Step 4: Output of Human-Centered Resilience Enhancement Strategies:

[0114] Using the decision of whether to reinforce each pipeline as a binary decision vector, and the total cost of pipeline reinforcement and the predicted cumulative hardship as dual objectives, the NSGA-II multi-objective evolutionary algorithm is employed for Pareto optimization. NSGA-II parameters include: population size. Evolutionary algebra Cross rate Variation rate Output a set of hardening strategies that minimize cumulative suffering of the population under constraints of different total hardening costs;

[0115] The expression for the bi-objective optimization is as follows:

[0116]

[0117] in

[0118]

[0119] To reinforce the total cost,

[0120]

[0121] Accumulate suffering for the average scenario predicted by the surrogate model. Size of the scene set.

[0122] In the above formula, each symbol is defined as follows: w is the binary hardening decision vector, and wk=1 indicates that pipe k is selected as the hardening target; The unit price for reinforcement of pipe k (yuan / km) is determined by the "Municipal Engineering Comprehensive Budget Quota - Water Supply and Drainage Engineering Volume" and local cost information according to pipe diameter. It comprehensively considers all reinforcement engineering costs, including materials, labor, machinery, earthwork excavation and backfilling, joint flexibility modification, and seismic supports. Specific values ​​are shown in Table 4 below. Lk is the length of pipe k; Np is the total number of pipes in the network; S is the Monte Carlo damage scenario set, |S| is the size of the scenario set; ΣT,s* is the cumulative suffering value predicted by the trained cumulative suffering surrogate model for the s-th scenario under reinforcement strategy w. The strategy selected on the Pareto front is the SLF optimal strategy. As a baseline, the second objective J2^hum is replaced with the mean value J2^eng of the SDI-AUC gap scenario predicted by the SDI-AUC surrogate model. The strategy set obtained under the same NSGA-II hyperparameters is called the SDI optimal strategy.

[0123] Step 5: Output and Robustness Verification of Human-Centered Resilience Enhancement Strategies: The optimal reinforcement strategy is extracted from the Pareto front based on budget constraints. The reinforcement effect of each strategy is reflected by adjusting the pipeline repair rate. Variance-based global sensitivity analysis (Sobol' index) is used to quantify the impact of key parameters such as disaster intensity, human-centered parameters, and budget level on the three output indicators, verifying the robustness of the human-centered conclusions relative to parameter uncertainty, thus completing the human-centered analysis and optimization method for improving the disaster resilience of water supply networks.

[0124] In this embodiment, step three uses a three-layer ReLU-MLP, AdamW optimization, L2 regularization, and early stopping training to create the SDI-AUC model feedforward artificial neural network (ANN) and cumulative suffering feedforward artificial neural network (ANN) surrogate models. The test set evaluation results show that the SDI-AUC surrogate model... , Cumulative Suffering Proxy Model , ( Figure 7 , Figure 8 The surrogate model's prediction accuracy meets the requirements for optimized applications.

[0125]

[0126] In this embodiment, step five, the global sensitivity analysis of the variance basis, uses the Sobol' exponent to quantify the impact of parameter uncertainty on the output index.

[0127]

[0128] Indicates parameters Variance ratio of individual contributions, total effect index;

[0129]

[0130] Include All interaction effects with other parameters (where Y is the model output index, X_i is the i-th uncertainty input parameter, and X_{-i} are all other input parameters except X_i) are estimated using the Jansen estimator combined with the quasi-random Sobol' sampling method. and The confidence intervals were obtained through Bootstrap resampling. The analysis included, but was not limited to, PGV intensity multiplication factor, tolerance level scaling factor, reinforcement budget level, Sigmoid steepness parameter and inflection point offset, to verify the weight of each parameter on the three indicators of water outage duration reduction rate, cumulative suffering reduction rate and recovery time reduction rate for high-risk groups.

[0131] The reinforcement strategy conclusions drawn from this embodiment are as follows:

[0132] (1) Pareto efficiency: As the reinforcement budget increased from 7 million yuan to 40 million yuan, the cumulative hardship decreased from 408 to 286.

[0133] (2) Strategy comparison Figure 9 Under a budget of RMB 18.03 million, the optimal SLF strategy (cumulative suffering 326, stabilizing on day 7) reduced cumulative suffering by 13% and shortened the recovery time by 2 days compared to the optimal SDI strategy (cumulative suffering 376, stabilizing on day 9); it also showed significant benefits compared to the baseline without enhancement (cumulative suffering 420, stabilizing on day 11).

[0134] (3) Risk stratification benefits ( Figure 10 , Figure 11 The optimal SLF strategy reduced water outage duration by 38.5% for high-risk groups, significantly outperforming the optimal SDI strategy's 27.8%, demonstrating a systematic advantage across all risk levels.

[0135] (4) Strategy differences: The optimal strategy of SLF tends to choose medium-diameter and shorter water distribution pipes, covering about 60% of the total population; the optimal strategy of SDI tends to choose large-diameter and longer main pipes, covering only about 40% of the total population; within the full budget range of RMB 70 million to RMB 40 million, the overlap index ESOI of the two strategies only increased from 0.11 to 0.61, indicating that there is a persistent and significant difference between the two.

[0136] (5) Robustness (parameter perturbation range is shown in Table 5): The PGV intensity multiplication factor is the most significant source of variance. The tolerance level scale factor is the second largest. ), Sigmoid parameter ( , The location of the epicenter has minimal impact. The human-centered conclusions remain robust across the entire range of parameter perturbations.

[0137] The key parameter values ​​and their basis for this embodiment are summarized in Tables 1-5 below.

[0138] Table 1. Values ​​of Pipe Correction Factor Cmat,k

[0139]

[0140] Table 2. Values ​​of pipe diameter correction factor Cdia,k

[0141]

[0142] Table 3. Parameters for daily water-related activities (used in the hardship level function)

[0143]

[0144] Table 4 Unit Cost of Pipeline Reinforcement (ck)

[0145]

[0146] Table 5. Perturbation Range of Sobol' Global Sensitivity Analysis Parameters

[0147]

Claims

1. A human-centered analysis and optimization method for improving the disaster resilience of water supply networks, characterized in that... The human-centered analysis and optimization method for improving the disaster resilience of water supply networks is implemented according to the following steps: Step 1: Disaster Risk Characterization and Pipeline Damage Scenario Generation Using the moment magnitude Mw, focal location, and focal depth of the scenario earthquake disaster as input, the median predicted peak ground velocity (PGV) of each water supply network node in the target area is calculated using the ground motion prediction equation; the logarithm of the median predicted value is then taken to obtain the logarithmic PGV. The total uncertainty of logarithmic PGV is decomposed into inter-event residuals and spatially correlated intra-field residuals. Two parts, thus constructing N spatially related ground sports fields; For each spatially related ground sports field, the water supply pipeline is calculated according to the power-law corrected restoration rate formula. Repair rate per unit length Thus, a water supply pipeline was obtained. Probability of damage ; The formula for the power-law correction rate is as follows: ； In the formula As the baseline repair rate, This is a normalized intensity reference value. For water supply pipes peak ground speed, This is the intensity scaling index. For material correction factors, This is the pipe diameter correction factor. For terrain correction factors, This is a liquefaction multiplicative correction factor; water supply pipes Probability of damage Based on conditional probability calculations, the water supply pipelines were obtained respectively. The probability of fracture and the probability of leakage are combined with Monte Carlo sampling to construct a large-scale pipeline damage scenario; Step Two: Post-Disaster Hydraulic Analysis and Quantification of Human Suffering For each pipeline damage scenario, the water supply pipeline is divided into three states: intact, broken, and leaking. The broken pipeline is isolated from the water supply network, and a virtual leak node is introduced for the leaking pipeline and the leakage flow is simulated to obtain the daily water supply of each node in the water supply network. Divide the daily water supply of a node by the population it serves to obtain the average daily water consumption per person. Greedily allocate the average daily water consumption per person according to different water-related daily activities. When the water consumption for a certain water-related daily activity is less than the minimum water demand, the deprivation time is accumulated daily. Then, a bounded sigmoid suffering degree function is used to map the accumulated deprivation time to the instantaneous suffering of the corresponding water-related daily activity. The instantaneous suffering at the node level is the sum of the instantaneous suffering of all water-related daily activities. The system-level instantaneous suffering is obtained by weighting all node-level instantaneous sufferings with the population served by the node as the weight. The system-level instantaneous suffering is obtained by summing the system-level instantaneous sufferings daily over the T-day recovery period. Step 3: Agent Model Construction and Multi-Objective Optimization The input feature is formed by splicing the three-state unique thermal encoding of the water supply pipeline with the global damage count. The global damage count is the total number of broken water supply pipelines and the total number of leaking water supply pipelines in the water supply network within the target area. The cumulative suffering ΣT* is the output feature. The cumulative suffering feedforward artificial neural network proxy model is trained to obtain the trained cumulative suffering proxy model. Step 4: Output of Human-Centered Resilience Enhancement Strategies: Based on the trained cumulative suffering surrogate model, the binary decision vector is used to determine whether to reinforce the water supply pipeline. The dual objectives are the total reinforcement cost and the cumulative suffering predicted by the trained cumulative suffering surrogate model. The Pareto optimization is performed using the NSGA-II multi-objective evolutionary algorithm to output a set of reinforcement strategies that minimize cumulative suffering under different total reinforcement cost constraints. This completes a human-centered analysis and optimization method for improving the disaster resilience of water supply networks.

2. The human-centered analysis and optimization method for improving the disaster resilience of water supply networks according to claim 1, characterized in that... The expression for the logarithm PGV of the water supply network nodes in step one is as follows: ； in, This is the midpoint prediction function in the ground motion prediction equation. For the first Joyner-Boore distance of the node For site and path parameter vectors, For the inter-event residuals, This represents the spatially correlated field residuals.

3. The human-centered analysis and optimization method for improving the disaster resilience of water supply networks according to claim 1, characterized in that... Water supply pipes in step one Probability of damage The calculation formula is: ； in For the length of the pipe, For water supply pipes Repair rate per unit length.

4. The human-centered analysis and optimization method for improving the disaster resilience of water supply networks according to claim 1, characterized in that... In step two, a virtual leakage node is introduced into the leaking pipe and the leakage flow rate is simulated. The simulated leakage flow rate is determined by the thin orifice equation: ； in The orifice coefficient, For the desired leakage area, It is the acceleration due to gravity. This refers to a localized water head.

5. The human-centered analysis and optimization method for improving the disaster resilience of water supply networks according to claim 1, characterized in that... Step two involves water-related daily activities, which are divided into five categories: drinking water, cooking, using the toilet, bathing, and washing.

6. The human-centered analysis and optimization method for improving the disaster resilience of water supply networks according to claim 1, characterized in that... Step two involves a bounded Sigmoid function to assess the degree of suffering. The expression is: in The upper limit of saturation, For steepness parameter, For water-related activities The cumulative duration of deprivation, It represents the inflection point of the bounded sigmoid function for the degree of suffering.

7. The human-centered analysis and optimization method for improving the disaster resilience of water supply networks according to claim 6, characterized in that... When the daily activity involving water is drinking water ρ is the shape parameter of the Yang exponential model, and TL drink Tolerance level for drinking water activities.

8. The human-centered analysis and optimization method for improving the disaster resilience of water supply networks according to claim 1, characterized in that... System-level instantaneous suffering in step two The expression is: in For water supply network nodes The service population, Let A be the set of all demand nodes, and let A represent different daily water-related activities.

9. The human-centered analysis and optimization method for improving the disaster resilience of water supply networks according to claim 1, characterized in that... In step three, the cumulative suffering feedforward artificial neural network surrogate model consists of an input layer, two hidden layers, and an output layer. The first hidden layer has 128 neurons, and the second hidden layer has 64 neurons, using the ReLU activation function.

10. The human-centered analysis and optimization method for improving the disaster resilience of water supply networks according to claim 1, characterized in that... In step four, the decision vector for whether to reinforce each pipeline is used, and the dual objectives are the total reinforcement cost of the water supply pipeline and the predicted cumulative hardness. The expression for the total reinforcement cost is as follows: ； in =1 indicates that pipe k is selected as the reinforcement target. Let the unit price for reinforcement be the unit length of pipe k. Let N be the length of pipe k. p This represents the total number of pipelines in the network.

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