A four-stage heuristic recovery method and a resilience evaluation system for post-earthquake water supply network

Abstract

The application discloses a four-stage heuristic recovery method and a resilience evaluation system for a post-earthquake water supply pipe network, and belongs to the technical field of urban infrastructure earthquake resistance resilience evaluation and recovery decision-making.The recovery process is divided into four progressive stages: a stage of repairing unavailable pump stations, a stage of repairing isolated nodes, a stage of repairing remaining disconnected pipelines, and a stage of repairing remaining leaking pipelines.A dynamic importance strategy is adopted for the disconnected pipelines to capture dynamic changes in functions, and a static importance strategy is adopted for the leaking pipelines to improve calculation efficiency.Through the four-stage progressive recovery and the mixed importance evaluation strategy, the application can ensure high resilience of the post-earthquake water supply pipe network, ensure that all users obtain basic water supply as soon as possible, and significantly improve the calculation efficiency, thereby providing fast and scientific response support for post-earthquake emergency decision-making.

Description

Technical Field

[0001] This invention relates to the field of seismic resilience assessment and recovery decision-making technology for urban infrastructure, and in particular to a four-stage heuristic recovery method and resilience assessment system for post-earthquake water supply networks. Background Technology

[0002] Water supply networks are critical lifeline infrastructure for maintaining the normal operation of cities, providing essential water resources for residential life, industrial production, and fire protection systems. However, due to their wide spatial distribution, complex structure, and extensive underground burial, earthquakes pose a serious threat to their normal operation. Post-earthquake water supply networks often suffer widespread damage, mainly including pump station damage, pipeline disconnection (complete flow interruption), and pipeline leakage (partial flow loss). Rapidly and effectively restoring the function of water supply networks is of significant social importance and urgent practical necessity for ensuring the basic water needs of residents after an earthquake and preventing secondary disasters (such as uncontrolled fires and deterioration of sanitation conditions).

[0003] Existing post-earthquake water supply network restoration models are mainly divided into the following three categories: The first type is the random recovery model, which randomly selects objects to be repaired from all damaged components, lacking a clear priority repair strategy. Although this type of model is simple to implement, its recovery efficiency is extremely low, and the pipeline network function recovery curve is flat, failing to meet the timeliness requirements of post-earthquake emergency response.

[0004] The second type is the static importance recovery model. Its core idea is to calculate the static importance index of all damaged pipelines once, based on the initial damage state of the pipeline network, before the recovery process begins. Then, the repair order is determined by sorting these indices from highest to lowest. This type of model has high computational efficiency, but it has a fundamental flaw: it ignores the changes in the pipeline network topology and functional state caused by repaired pipelines, as well as the resulting dynamic changes in the importance of unrepaired pipelines, leading to limited overall resilience improvement.

[0005] The third type is the dynamic importance recovery model. This type of model reassesses the importance of all remaining damaged pipelines before each repair decision, accurately capturing the dynamic evolution of the pipeline network's functional state and thus achieving a higher final resilience level. However, its computational cost increases exponentially with the intensity of the earthquake. When the earthquake intensity is high (e.g., 0.55g), the analysis time can be more than ten times that of the static importance model, severely affecting the timeliness of post-earthquake emergency decision-making.

[0006] Furthermore, existing recovery models generally neglect the issue of resource accessibility in the initial recovery phase. Whether static or dynamic importance models, their optimization objective is to maximize the overall recovery speed of the pipeline network, thus prioritizing the repair of damaged pipelines that can maximize overall functional indicators. These pipelines are typically located in central areas or main pipeline sections that already contain pumping stations. This results in isolated nodes far from water sources being without water for extended periods, creating the so-called "island effect," where some residents are completely without water in the initial recovery phase. While this recovery strategy appears to restore overall system functional indicators quickly, it contradicts the social need to "ensure every resident has access to basic water as soon as possible" and the people-centered recovery philosophy during the post-earthquake emergency phase.

[0007] In summary, how to significantly improve computational efficiency while ensuring the high resilience of the post-earthquake water supply network, and at the same time ensure that all users can obtain basic water supply in the early stages of recovery, is a technical challenge that urgently needs to be solved in this field. Summary of the Invention

[0008] The purpose of this invention is to provide a four-stage heuristic recovery method and resilience assessment system for post-earthquake water supply networks, in order to solve the technical problem that existing recovery models cannot simultaneously take into account high resilience, high computational efficiency, and resource accessibility of all nodes in the early stage of recovery.

[0009] To achieve the above objectives, this invention provides a four-stage heuristic restoration method for post-earthquake water supply networks, comprising the following steps: Step S1: Based on the seismic intensity parameters, generate the initial damage status of each pumping station and pipeline in the post-earthquake water supply network; the damage status includes the availability / unavailability of the pumping stations, as well as the disconnection and leakage points on the pipelines.

[0010] Step S2: First-stage recovery: Identify unavailable pump stations, use a dynamic importance strategy to determine the repair order, and repair them sequentially.

[0011] Step S3: Second-stage recovery: Identify isolated nodes, which are pump stations or user connection areas that have lost hydraulic connection with the main network area containing available pump stations; for each isolated node, repair only the break point on the damaged pipeline with the highest dynamic importance that connects it to the main network area to restore the connectivity of the isolated node.

[0012] Step S4: Third-stage recovery: Using a dynamic importance strategy, determine the repair order for all unrepaired disconnected and damaged pipelines and repair them sequentially.

[0013] Step S5: Fourth-stage recovery: Using a static importance strategy, based on the network status when the third-stage repair is completed, determine the repair sequence for all remaining leaking and damaged pipelines and repair them sequentially.

[0014] The dynamic importance strategy updates the dynamic importance value of the components to be repaired in real time based on the current pipeline functional status before each repair decision; the static importance strategy calculates the static importance value of all components to be repaired only once when the pipeline functional status is completed in the third stage of repair.

[0015] Preferably, in step S1, the damage state of the pumping station is determined based on a log-normal distribution vulnerability model. The vulnerability model of the pumping station is calculated using the following formula: (1); In the formula, The probability of a pump station reaching or exceeding a specific failure state under a given seismic intensity; Peak ground acceleration; It is the standard normal distribution function; and The first Median and log-standard deviation of damage level; The damage status of the pumping station. = 1, 2, 3, 4 correspond to minor, moderate, severe and complete damage respectively. The pump station can operate normally when there is minor damage, but cannot be used when there is moderate or severe damage. DS This represents the actual damage state of the pump station under seismic loading.

[0016] The damage status of the pipeline is determined based on the repair rate model. The vulnerability model of the pipeline is calculated using the following formula: (2); (3); In the formula, The intensity of the ground motion; Standard repair rate; This is the pipe diameter correction factor; This is the pipe material correction factor; This is a site topography correction factor; This is the site liquefaction correction factor; This represents the actual repair rate.

[0017] The number of damage points on the damaged pipeline follows a Poisson distribution: (4); In the formula, This represents the number of damage points on a given pipeline. This is the length of the pipeline.

[0018] The probability of the damage point being a break point is 20%, and the probability of it being a leakage point is 80%.

[0019] (5); In the formula, P d This represents the probability that a certain pipeline will be damaged after an earthquake.

[0020] Spacing between adjacent damage points on the damaged pipeline satisfy: (6); In the formula, The specific location of the damage point is determined by Monte Carlo sampling using uniformly random numbers within the interval (0, 1).

[0021] Preferably, in step S3, the isolated pumping station is defined as: a functional pumping station whose directly connected pipelines contain at least one disconnection point, preventing it from supplying water to the pipe network; the isolated user connectivity area is defined as: a connectivity component consisting of user nodes whose pipelines connected to all pumping station components contain at least one disconnection point.

[0022] For multiple damaged pipelines connecting isolated pumping stations to the main pipeline network, the dynamic importance of each damaged pipeline is calculated separately, and only the damaged pipeline with the highest dynamic importance is repaired. Similarly, for multiple damaged pipelines connecting isolated user areas to pumping station components, only the damaged pipeline with the highest dynamic importance is repaired. If multiple isolated pumping stations or multiple isolated user areas exist simultaneously, the dynamic importance of their respective target damaged pipelines is calculated separately, and they are repaired sequentially from highest to lowest value.

[0023] Preferably, the dynamic importance is calculated using the following formula: (7); (8); The static importance is calculated using the following formula: (9); In the formula, For damaged pumping stations Dynamic importance; For damaged pipelines Dynamic importance; For damaged pipelines Static importance; The overall functional value of the water supply network before the target component is repaired; The overall functional value of the water supply network after the target component is repaired; For pumping stations Repair time; For pipelines Repair time.

[0024] Preferably, in step S4, for multiple break points on the same damaged pipeline, they are repaired sequentially according to their position along the pipeline. In step S5, for multiple leakage points on the same damaged pipeline, if their static importance is the same, they are repaired sequentially according to their position along the pipeline.

[0025] Preferably, the overall functional value of the water supply network Simultaneously, calculations are performed based on the node's water supply and node water pressure: (10); In the formula, Number the pipeline nodes; For nodes Pre-earthquake water supply; For nodes The actual water supply after the earthquake; For nodes The pre-earthquake water supply pressure; For nodes Post-earthquake water supply pressure; For nodes The weighting coefficients are determined according to the proportion of pre-earthquake water demand. Weighting coefficients for water supply indicators at nodes; The weighting coefficients for the node pressure index.

[0026] Preferred, node Actual water supply after the earthquake Calculations were performed using a pressure-driven water demand model: (11); In the formula, For nodes The actual water pressure after the earthquake; For nodes Minimum service water pressure; For nodes Standard service water pressure; For nodes Pre-earthquake water supply; For nodes The actual water supply after the earthquake.

[0027] Preferably, in steps S2 to S5, the repair time for each damaged component is determined according to the HAZUS model: for pump stations, the repair time follows a normal distribution, with a mean of 3.1 days and a standard deviation of 2.7 days for moderate damage, a mean of 13.5 days and a standard deviation of 10 days for severe damage, and a mean of 35 days and a standard deviation of 18 days for complete failure; for pipelines, the repair time for a single disconnection point is 12 hours when the pipe diameter is less than 305 mm and 20 hours when the pipe diameter is greater than or equal to 305 mm; the repair time for a single leakage point is 6 hours when the pipe diameter is less than 305 mm and 10 hours when the pipe diameter is greater than or equal to 305 mm.

[0028] Preferably, the method further includes step S6: based on the repair sequence generated in steps S2 to S5, plotting a functional recovery curve of the overall pipeline network functional value as a function of repair time. The toughness index RI is calculated using the following formula: (12); In the formula, The time after the earthquake; For the aftermath of the earthquake The overall functional value of the pipeline network at any given time; The time when the earthquake occurred; The point at which the pipeline network function recovers to pre-earthquake levels; This is the pipeline network resilience index.

[0029] The present invention also provides a post-earthquake water supply network resilience assessment system using the above method, comprising: The earthquake damage analysis module is used to perform step S1 to generate random damage scenarios; The hydraulic analysis module is used to build hydraulic models of disconnected and leaking pipelines, and to calculate the water supply at nodes using a pressure-driven water demand model. The functional evaluation module is used to calculate the overall functional value of the pipeline network based on the node water supply and node water pressure. The four-stage heuristic recovery module is used to execute steps S2 to S5 to generate the recovery sequence of each damaged component; The resilience index calculation module is used to perform step S6 to calculate the pipeline network resilience index. When executing the dynamic importance strategy, the four-stage heuristic recovery module calls the hydraulic analysis module and the functional evaluation module in real time to obtain the current pipeline network functional status.

[0030] Preferably, in the hydraulic analysis module, a leakage hydraulic model including virtual nodes, virtual pipelines, and check valves is constructed for the leakage failure point; and a flow interruption hydraulic model including virtual pipelines and check valves is constructed for the disconnection failure point.

[0031] Specifically, for pipelines with single-point leakage, a new leakage point is added to the original pipeline AB. New pipelines , and ,exist Install a check valve on top so that water can only flow from... Flow towards virtual reservoir R. Flow loss due to seepage and damage. Calculate using the following formula: (13); In the formula, The orifice flow coefficient has a value ranging from 0.6 to 0.9. The leakage area; The water head at the leakage point; The virtual reservoir head is set to 0; is the local loss coefficient, taken as 1; g is the gravitational acceleration, taken as 9.8 m / s². 2 .

[0032] For a single-point disconnected pipeline, virtual pipelines are added at both ends A and B of the original pipeline AB. and ,exist and Install check valves on each of the above to ensure that water can only flow from A to [the destination]. Flowing from B to Traffic loss caused by disconnection / damage Calculated using the Hazen-Williams formula: (14); In the formula, This refers to the pipe roughness coefficient. The diameter of the pipe; This refers to the length of the pipe. End point head; To disconnect the water head at the point of failure.

[0033] For pipelines with multiple leakage points and multiple disconnection points, first identify the two disconnection points closest to each end of the pipeline and establish hydraulic models for these two disconnection points; for leakage points between the two ends and their respective nearest disconnection points, establish leakage hydraulic models separately; the pipe section between the two nearest disconnection points is considered invalid because no water flows through it and is not included in the subsequent hydraulic analysis.

[0034] Therefore, the present invention, employing the above-described four-stage heuristic recovery method and resilience assessment system for post-earthquake water supply networks, possesses the following beneficial effects: (1) By setting up a second phase to prioritize the repair of isolated nodes, this invention ensures that all user nodes can obtain basic water supply as early as possible in the initial recovery phase, effectively avoiding the "island effect" common in the post-earthquake recovery process, and is more in line with the people-oriented social needs in the post-earthquake emergency phase.

[0035] (2) The present invention adopts a dynamic importance strategy for disconnection failure points to ensure high toughness, and adopts a static importance strategy for leakage failure points to significantly reduce the amount of computation, thus achieving an organic unity of high toughness and high computational efficiency.

[0036] (3) The present invention uses a four-stage progressive recovery and mixed importance assessment strategy. Under the condition of 0.55g seismic intensity, the calculation time is only about one-tenth of that of the pure dynamic importance model, while the toughness index is only about 4% different. It can provide rapid and scientific response support for post-earthquake emergency decision-making. It is also applicable to pipeline toughness assessment and reinforcement scheme optimization in the pre-earthquake planning stage.

[0037] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0038] Figure 1 This is a technical roadmap for a four-stage heuristic recovery method and resilience assessment system for post-earthquake water supply networks according to the present invention. Figure 2 This is a reference model diagram of a water supply network in an embodiment of a four-stage heuristic recovery method and resilience assessment system for post-earthquake water supply networks according to the present invention. Figure 3 This is a diagram showing the seismic vulnerability curve of a pumping station in an embodiment of a four-stage heuristic recovery method and resilience assessment system for post-earthquake water supply networks according to the present invention. Figure 4 This is a schematic diagram of the hydraulic model of the pipeline leakage failure point in an embodiment of the four-stage heuristic recovery method and resilience assessment system for post-earthquake water supply networks of the present invention. Figure 5 This is a schematic diagram of the hydraulic model of the pipeline disconnection and failure point in an embodiment of the four-stage heuristic recovery method and resilience assessment system for post-earthquake water supply networks of the present invention. Figure 6 This is a schematic diagram of the four-stage recovery process and resilience index calculation of a water supply network in an embodiment of the four-stage heuristic recovery method and resilience assessment system for post-earthquake water supply networks of the present invention. Figure 7 This is a comparison of the functional recovery curves of different recovery models under a 0.55g seismic intensity in an embodiment of the four-stage heuristic recovery method and resilience assessment system for post-earthquake water supply networks of the present invention. Figure 8This is a comparison chart of the network toughness index of different recovery models under different seismic intensity in an embodiment of the four-stage heuristic recovery method and toughness assessment system for post-earthquake water supply networks of the present invention. Figure 9 This is a comparison of analysis time for different recovery models under a 0.55g seismic intensity in an embodiment of the four-stage heuristic recovery method and resilience assessment system for post-earthquake water supply networks of the present invention. Detailed Implementation

[0039] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0040] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0041] Example like Figure 1 As shown, this embodiment uses the water supply network of a medium-sized city in China as the application object to provide a detailed description of the method and system of the present invention: S1. Pipeline network model and basic parameters: This embodiment uses a benchmark model of the water supply network of a medium-sized city in China (see [link]). Figure 2 The city is located on the southeastern coast of China, with an area of ​​345 km². 2 The area has a population of 690,000 and a seismic fortification intensity of VII. The site is an alluvial plain, free from geological hazards such as soil liquefaction. The pipeline network comprises 188 nodes (2 pumping station nodes and 186 user nodes) and 319 pipes. Pipe diameters range from 200 mm to 1000 mm, and pipe materials include cast iron pipes (C=100) and PVC pipes (C=150). The two pumping stations, PBS1 and PBS2, operate at pressures of 38 m³ and 35 m³, respectively, and the daily water supply is provided jointly by both stations.

[0042] The pump station vulnerability parameters used in this embodiment are shown in Table 1, the recovery time parameters of the pump station and pipeline are shown in Table 2 and Table 3 respectively, and the pipe diameter, material, quantity, length and roughness parameters of the water supply network are shown in Table 4.

[0043] Table 1. Damage status and seismic vulnerability parameters of the pumping station

[0044] Table 2. Pump Station Recovery Time Parameters

[0045] Table 3. Pipeline recovery time parameters

[0046] Table 4. Water supply network parameters

[0047] S2. Post-earthquake damage scene generation: The ground motion intensity PGA was set to 0.2g, 0.25g, 0.3g, 0.35g, 0.4g, 0.45g, 0.5g and 0.55g, and 1000 Monte Carlo simulations were performed for each intensity.

[0048] The hydraulic models of the leakage and disconnection points on a damaged pipeline AB after the earthquake are shown below. Figure 4 and 5 As shown. Among them, and These are the flow rates at the two ends A and B of the pipeline, respectively. and It is divided into virtual reservoir 1 and virtual reservoir 2. and They are one-way check valve 1 and one-way check valve 2. It refers to the loss of leakage flow at the point of leakage failure. and It refers to the flow loss on both sides of the disconnection point.

[0049] A typical simulation with PGA=0.55g is used as an example for detailed explanation. The probability of each pump station reaching or exceeding each damage level is calculated based on Table 1 and Equation (1): ; The damage state was determined using uniformly distributed (0, 1) random numbers generated using the Monte Carlo method. In this simulation, the damage state of PBS1 was moderate (unrunnable), and that of PBS2 was slight (runnable). Figure 3 and Figure 6 As shown. Then, the actual repair rate of each pipeline is calculated according to equations (2) and (3). : ; ; The number of pipeline damage points is generated, and the type (disconnection or leakage, with a disconnection probability of 20% and a leakage probability of 80%) and specific location of each damage point are determined. Specifically, the number of damage points on the damaged pipeline follows a Poisson distribution according to equation (4): ; The distance between adjacent damage points is determined according to formula (6): ; in, The values ​​are uniformly random numbers within the interval (0, 1). This forms a detailed damage scenario.

[0050] S3, Detailed Explanation of the Four-Stage Recovery Process: S31. First phase: Repair unusable pump stations: In this simulation, only PBS1 was unusable (moderate damage). According to Table 2, the repair time for moderate damage is taken as a random sample of a normal distribution N(3.1, 2.7^2), assuming a sample value of 2.8 days. Directly repairing PBS1 takes 2.8 days. After repair, the hydraulic status and functional values ​​of the pipeline network are updated.

[0051] S32. Second phase: Repairing isolated nodes: This phase contains two sub-phases, as follows: Sub-phase one involves repairing the isolated pump station. After completing the first phase, PBS2 will be functional, but a break point exists on its only connecting pipe, ID:19, rendering PBS2 an isolated pump station. An isolated pump station is defined as: a functional (or repaired) pump station whose all directly connected pipes contain at least one break point, preventing it from supplying water to the network. Identify the broken pipe connecting PBS2 to the main network area (ID:19 only) and repair the break point on this pipe (see hydraulic model). Figure 5 The leak points will be repaired in the fourth stage. After repair, PBS2 will be connected to the main pipeline.

[0052] Sub-phase two involves repairing isolated user connectivity areas. Isolated user connectivity areas are identified, defined as: a connectivity component consisting of user nodes, where all pipelines connected to pump station components contain at least one point of disconnection. For example, the area consisting of user nodes 1, 2, 3, and 5 (e.g., ...). Figure 6 The purple area shown in the image represents an isolated user connectivity region. This region has disconnection points with the connecting pipes IDs 6, 7, and 8, which contain the pump station components. The dynamic importance of these three pipes is calculated according to equation (7): ; Assuming pipe 7 has the highest dynamic importance, repairing only the break point on pipe ID:7 will restore connectivity to that area. If multiple isolated areas exist simultaneously, the dynamic importance of each target pipeline is calculated and repaired sequentially from highest to lowest. After this step, all isolated nodes are connected, ensuring that each user node receives water supply (although the water volume may be insufficient).

[0053] S33, Third Stage: Repairing the remaining disconnected and damaged pipelines: After completing the second stage, the basic connectivity of the pipeline network is satisfied, but there are still disconnected or damaged pipelines in the network (such as ID: 2, 6, 8, 17, etc.). In the third stage, the dynamic importance of all remaining disconnected or damaged pipelines is calculated according to equation (8). Updated in real time based on the current pipeline network functional status: ; The first calculation revealed that pipe 17 If the connection is highest, then all disconnected or damaged points on it should be repaired first. After repair, the network topology is updated, and then the remaining disconnected or damaged pipelines are recalculated. Repair them sequentially until all disconnected or damaged points are repaired. For multiple disconnected or damaged points on the same damaged pipeline, repair them sequentially according to their location along the pipeline.

[0054] S34, Fourth Stage: Repairing remaining leaking and damaged pipelines: Finally, there are still leaking or damaged pipelines in the network (such as ID: 1, 11, 13, 17, 18, etc.). At this point, the static importance of all leaking or damaged pipelines is calculated at once according to equation (9): ; according to Sort by size from largest to smallest, and repair the leakage points on them in turn (see hydraulic model). Figure 4 For multiple leakage points on the same pipeline (e.g., pipeline 13 has 3 leakage points), if they have the same static importance, they can be repaired sequentially according to their location on the pipeline.

[0055] S4. Functional recovery curve and resilience assessment: After each repair step is completed, a hydraulic analysis and functional assessment are performed.

[0056] In the hydraulic analysis, a leakage hydraulic model including virtual nodes, virtual pipelines, and check valves is constructed for the leakage failure point according to equation (13): ; Construct a flow interruption hydraulic model including virtual pipelines and check valves for the disconnection failure point (14): ; The actual water supply at each node is calculated using the pressure-driven water demand model of equation (11): ; In the functional assessment, the overall functional value of the pipeline network is calculated based on the node water supply and node water pressure according to equation (10): ; Record the network function value after each repair step is completed, plot the water supply network function recovery curve, and finally calculate the resilience index according to formula (12): ; S5. Comparison results of different recovery models: To verify the superiority of the present invention, the four-stage heuristic recovery model of the present invention is compared with three benchmark models: stochastic recovery model, static importance recovery model, and dynamic importance recovery model.

[0057] Comparison of functional recovery curves: such as Figure 7 As shown, in Under the given conditions, in the initial recovery phase (0-308 hours), the functional recovery slope of this invention is slightly lower than that of the static and dynamic importance models. This is because this invention prioritizes repairing isolated nodes in the second stage to restore connectivity rather than maximizing functional value. However, after completing the second stage (approximately 308 hours), all isolated nodes are connected, and the functional recovery curve of this invention surpasses that of the static importance model and gradually approaches that of the dynamic importance model. Meanwhile, the static importance model still has isolated nodes at this point, and its functional recovery curve is significantly lower than that of this invention.

[0058] Comparison of resilience indices: such as Figure 8 As shown, in Under the conditions, the toughness index of the present invention Far superior to random models and static model And it is very close to the dynamic model. .

[0059] Computational efficiency comparison: such as Figure 9 As shown, the computation time of this invention is 23.98 seconds, which is only about one-tenth of that of the dynamic model (229.69 seconds) and is on the same order of magnitude as that of the static model (17.64 seconds).

[0060] The above verification results show that the present invention significantly improves computational efficiency while ensuring high toughness, and enables all user nodes to receive water supply earlier after the earthquake, which is more in line with the social needs of the post-earthquake emergency phase.

[0061] S6. System Integration and Application Scenarios: The method described in this invention can be integrated into a post-earthquake water supply network resilience assessment system, comprising a seismic damage analysis module, a hydraulic analysis module, a functional assessment module, a four-stage heuristic recovery module, and a resilience index calculation module. This system can rapidly generate recovery plans after an earthquake and can also be used in the pre-earthquake planning stage to assess the resilience of the network and optimize reinforcement schemes.

[0062] Working Principle: This invention follows the recovery principle of "resource accessibility first, functional restoration second," and achieves a unified approach of high resilience, high computational efficiency, and full node resource accessibility during the post-earthquake water supply network restoration process through a four-stage progressive restoration and hybrid importance assessment strategy. The first stage prioritizes repairing unusable pumping stations to restore water supply capacity; the second stage prioritizes repairing critical pipelines connecting isolated nodes to ensure basic water accessibility for all users; the third stage employs a dynamic importance strategy to repair disconnected and damaged pipelines to efficiently improve the overall function of the network; and the fourth stage employs a static importance strategy to repair leaking and damaged pipelines to reduce computational overhead. This method balances social benefits (full node resource accessibility), recovery effectiveness (high resilience), and decision-making timeliness (high computational efficiency), providing scientific and rapid technical support for post-earthquake emergency decision-making.

[0063] Therefore, the present invention provides a four-stage heuristic recovery method and resilience assessment system for post-earthquake water supply networks with the above-mentioned structure, which has outstanding advantages such as ensuring resource accessibility at all nodes, balancing high resilience and high computational efficiency, and supporting rapid emergency response.

[0064] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A four-stage heuristic restoration method for post-earthquake water supply networks, characterized in that, Includes the following steps: Step S1: Based on the seismic intensity parameters, generate the initial damage status of each pumping station and pipeline in the post-earthquake water supply network; Damage status includes the availability / unavailability of the pump station, as well as disconnection and leakage points on the pipeline; Step S2: First-stage recovery: Identify unavailable pump stations, use a dynamic importance strategy to determine the repair order, and repair them sequentially; Step S3: Second-stage recovery: Identify isolated nodes, which are pump stations or user connection areas that have lost hydraulic connection with the main network area containing available pump stations; for each isolated node, repair only the break point on the damaged pipeline with the highest dynamic importance that connects it to the main network area to restore the connectivity of the isolated node. Step S4: Third-stage recovery: Using a dynamic importance strategy, determine the repair order for all unrepaired disconnected and damaged pipelines and repair them sequentially; Step S5: Fourth stage recovery: Using a static importance strategy, based on the network status when the third stage of repair is completed, determine the repair sequence for all remaining leaking and damaged pipelines and repair them sequentially. The dynamic importance strategy updates the dynamic importance value of the components to be repaired in real time based on the current pipeline functional status before each repair decision; the static importance strategy calculates the static importance value of all components to be repaired only once based on the pipeline functional status when the third stage of repair is completed.

2. The four-stage heuristic restoration method for post-earthquake water supply networks according to claim 1, characterized in that, In step S1, the damage status of the pump station is determined based on the vulnerability model of the log-normal distribution; the damage status of the pipeline is determined based on the repair rate model. The number of damage points on the pipeline follows a Poisson distribution, and each damage point has a 20% probability of being a disconnection failure point and an 80% probability of being a leakage failure point.

3. The four-stage heuristic restoration method for post-earthquake water supply networks according to claim 1, characterized in that, In step S3, an isolated pump station is defined as: a functional pump station whose directly connected pipelines contain at least one disconnection point; an isolated user connectivity area is defined as: a connectivity component of a user node whose pipelines connected to all components containing pump station contain at least one disconnection point.

4. The four-stage heuristic restoration method for post-earthquake water supply networks according to claim 1, characterized in that, Dynamic importance is calculated using the following formula: ； ； Static importance is calculated using the following formula: ； In the formula, For damaged pumping stations Dynamic importance; For damaged pipelines Dynamic importance; For damaged pipelines Static importance; The overall functional value of the water supply network before the target component is repaired; The overall functional value of the water supply network after the target component is repaired; For pumping stations Repair time; For pipelines Repair time.

5. The four-stage heuristic restoration method for post-earthquake water supply networks according to claim 4, characterized in that, Overall functional value of water supply network Simultaneously, calculations are performed based on the node's water supply and node water pressure: ； In the formula, Number the pipeline nodes; For nodes Pre-earthquake water supply; For nodes The actual water supply after the earthquake; For nodes The pre-earthquake water supply pressure; For nodes Post-earthquake water supply pressure; For nodes The weighting coefficients are determined according to the proportion of pre-earthquake water demand. Weighting coefficients for water supply indicators at nodes; The weighting coefficients for the node pressure index.

6. The four-stage heuristic restoration method for post-earthquake water supply networks according to claim 5, characterized in that, node Actual water supply after the earthquake Calculations were performed using a pressure-driven water demand model: ； In the formula, For nodes The actual water pressure after the earthquake; For nodes Minimum service water pressure; For nodes Standard service water pressure; For nodes Pre-earthquake water supply; For nodes The actual water supply after the earthquake.

7. The four-stage heuristic restoration method for post-earthquake water supply networks according to claim 1, characterized in that, In steps S2 to S5, the repair time for each damaged component is determined according to the HAZUS model: for pump stations, the repair time follows a normal distribution; for pipelines, the repair time for a single disconnection point is 12 hours or 20 hours depending on the pipe diameter, and the repair time for a single leakage point is 6 hours or 10 hours depending on the pipe diameter.

8. The four-stage heuristic restoration method for post-earthquake water supply networks according to claim 1, characterized in that, The process also includes step S6: Based on the repair sequence generated in steps S2 to S5, plot the functional recovery curve of the overall pipeline network functional value as a function of repair time. The toughness index is calculated using the following formula. : ； In the formula, The time after the earthquake; For the aftermath of the earthquake The overall functional value of the pipeline network at any given time; The time when the earthquake occurred; The point at which the pipeline network function recovers to pre-earthquake levels; This is the pipeline network resilience index.

9. A post-earthquake water supply network resilience assessment system employing the method described in any one of claims 1 to 8, characterized in that, include: The earthquake damage analysis module is used to perform step S1 to generate random damage scenarios; The hydraulic analysis module is used to build hydraulic models of disconnected and leaking pipelines, and to calculate the water supply at nodes using a pressure-driven water demand model. The functional evaluation module is used to calculate the overall functional value of the pipeline network based on the node water supply and node water pressure. The four-stage heuristic recovery module is used to execute steps S2 to S5 to generate the recovery sequence of each damaged component; The resilience index calculation module is used to perform step S6 to calculate the pipeline network resilience index. When executing the dynamic importance strategy, the four-stage heuristic recovery module calls the hydraulic analysis module and the functional evaluation module in real time to obtain the current network functional status.

10. The post-earthquake water supply network resilience assessment system according to claim 9, characterized in that, In the hydraulic analysis module, a leakage hydraulic model containing virtual nodes, virtual pipelines, and check valves is constructed for the leakage failure point; and a flow interruption hydraulic model containing virtual pipelines and check valves is constructed for the disconnection failure point.

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