A dynamic risk-based decision support method for long-term maintenance of water supply networks

Abstract

The present invention relates to the technical field of water supply network, and provides a long-term maintenance decision support method for water supply network based on dynamic risk, which includes the following steps: S1: building a data set; S2: building a partition model, grouping the pipelines with the GN algorithm, and after determining the partition result, selecting a set of weight group values ​​of the relevant partitions according to the demand; S3: quantifying the risk of each pipeline, it is necessary to first quantify the failure probability and failure consequence of the pipeline; S4: building a demand analysis module, after obtaining multiple maintenance demand sequence schemes, the management personnel conduct a scheme comparison analysis according to the demand; S5: building a performance evaluation model, so as to objectively evaluate the implementation effect of the framework; S6: the manager needs to select the best maintenance sequence from many alternative maintenance demand sequences, so as to formulate the final maintenance plan. The present invention can effectively help water management personnel make daily maintenance decisions for WDN.

Description

Technical Field

[0001] The present invention relates to the technical field of water supply pipe networks, and in particular to a dynamic risk-based long-term maintenance decision support method for water supply networks. Background Art

[0002] As an important part of critical infrastructure, water distribution networks (WDNs) play a vital role in improving the quality of life of citizens and ensuring socio-economic functions. Their failures can have devastating impacts on the city's safety, economy, and public health. However, water infrastructure and related equipment continue to deteriorate during use. The deterioration of pipelines leads to a gradual increase in leakage accidents, which in turn leads to rising maintenance costs. In order to ensure the sustainable operation of WDNs within financial constraints, it is urgent to adopt a full life cycle perspective to plan and execute future maintenance work of WDNs based on effective preventive long-term maintenance decisions.

[0003] In the process of making preventive long-term maintenance decisions, facing newly commissioned WDNs or those with only current status data, it is necessary to consider their future long-term maintenance planning. In this process, a time-based degradation model should be introduced, and simulation data should be used to simulate the degradation process of WDN in future long-term operation. The simulation data can simulate the corrosion changes of the pipe wall over time, the changes in leakage water flow and the changes in water pressure in the pipeline, etc., which can better understand the changes in risk value and performance of WDN in future daily degradation. The risk quantification of pipelines depends on the probability of failure and the consequences of failure. At present, a large number of relevant literatures have been studied on the calculation of the probability of failure and the consequences of failure of a single pipeline, forming a relatively mature research system.

[0004] At present, there are many literatures that make pipeline maintenance decisions based on risk assessment. However, in real life, pipeline maintenance is not completed in one go, but is affected by time sequence. The hydraulic conditions of WDN are complex. After repairing some pipelines, the first maintained pipelines will affect the hydraulic performance of the remaining pipelines to be maintained. At the same time, the failure probability and risk value of the repaired pipelines will drop to a certain range. At this time, it is necessary to recalculate the updated risk value of the pipeline to determine the next maintenance action, which will affect the maintenance order of the pipeline. However, after literature research, it was found that the current research on pipeline maintenance decision-making based on risk assessment mainly tends to directly formulate maintenance decision plans based on the static risk value obtained from the assessment, without fully considering the dynamic changes brought about by the maintenance action to the risk value, and the quantification of the specific maintenance scale in the decision-making.

[0005] Generally, the WDN repair problem is a multi-objective optimization problem. Under financial constraints, priority should be given to the maintenance of the pipelines with the highest risk value in the WDN, while considering the impact of cost, implementing effective infrastructure asset management, and making more comprehensive maintenance decisions to promote sustainable development. Therefore, in order to comprehensively consider dynamic risk value and cost optimization, when deciding whether to perform maintenance actions on the pipeline, it is necessary to consider the failure probability of the pipeline, the consequences of failure, the importance of the pipeline in the entire WDN, and the impact of the dynamic changes in risk value on the decision. Since the preventive long-term maintenance decision of WDN needs to consider the above four factors, a systematic framework is needed for effective asset management. At present, a large number of long-term preventive maintenance decision models have been developed. These decision models can comprehensively consider the potential combination of different decision factors to make the best multi-objective infrastructure maintenance decisions. These decision factors mainly include pipeline failure probability, risk analysis, life cycle cost and WDN topology analysis. These methods provide good help for managers to manage WDN infrastructure assets and make effective preventive maintenance decisions. However, these method frameworks have high data requirements and are mostly not suitable for WDNs that are newly put into use or have only current status data. Summary of the invention

[0006] The present invention provides a dynamic risk-based long-term maintenance decision support method for a water supply network, which can overcome certain defects of the prior art.

[0007] According to a dynamic risk-based long-term maintenance decision support method for a water supply network of the present invention, the method comprises the following steps:

[0008] S1: Build the dataset;

[0009] S2: Establish a partition model, use the GN algorithm to group the pipelines, and after determining the partition results, select a set of weight groups for the relevant partitions as required;

[0010] S3: To quantify the risk of each pipeline, it is necessary to first quantify the failure probability P of the pipeline f and failure consequences C f ;

[0011] S4: After building a demand analysis module and obtaining multiple maintenance demand sequence plans, the management personnel conduct comparative analysis of the plans based on the needs;

[0012] S5: Establish a performance evaluation model to objectively evaluate the implementation effect of the framework;

[0013] S6: Managers need to select the best maintenance sequence from many alternative maintenance requirement sequences to develop a final maintenance plan.

[0014] Preferably, in S1, the data set includes the topological structure of the WDN, the water demand of each node, the water supply conditions, the age of each pipeline, the pipe material, the burial depth, the land use and the soil type.

[0015] Preferably, in S2, the specific steps are as follows:

[0016] S21: Based on the existing WDN graph topology information, the GN algorithm is used to partition and cluster the WDN pipelines. By continuously removing the edges with the largest edge betweenness centrality EBC from the network, the remaining pipelines are the community pipelines. EBC is calculated using formula (1):

[0017]

[0018] where EBC(l) = betweenness centrality of edge l; τ s,t (l) = the number of shortest paths between nodes s and t that pass through edge l; τ s,t = the total number of shortest paths from node s to node t; V and E represent the set of nodes and edges respectively;

[0019] S22: Determine the partitioning results and visualize the partitioning effects using the WNTR library and Matplotlib library;

[0020] S23: The manager chooses a set of appropriate weight values ​​ω based on his or her preference, focusing on repairing adjacent community pipelines or repairing vital pipelines with high risk values. D and ω R .

[0021] Preferably, in S3, the specific steps are as follows:

[0022] S31: Calculate the failure probability P of the pipeline using the physical probability failure model f ;The failure probability model used considers the relationship between the maximum stress σ on the pipeline and the tensile strength of the pipeline material to calculate the pipeline brittleness curve;

[0023] S32: Calculate the pipeline failure consequence value C using the pipeline failure consequence quantification model f The pipeline failure consequence quantification model used comprehensively analyzes the economic, operational, environmental and social consequences of each pipeline failure based on 14 factors, and then quantifies the overall consequences of each pipeline failure;

[0024] S33: Known failure probability P f and failure consequences C f , then the comprehensive risk R of each pipeline failure can be determined f ; The equation widely used to quantify risk is to multiply the probability of failure by the consequence of failure, as shown in formula (2):

[0025] R f =P f ×C f (2)

[0026] S34: Get the risk value R f After that, we need to calculate the R f Set up a leaky model leak The leakage model is shown in formula (3), which introduces the risk value R of the pipeline f , so that the leakage flow of each pipe will change with the water pressure p and risk value R f Changes occur, as shown in formula (3):

[0027]

[0028] Among them, d leak is the leakage flow, A is the leakage area, C d is the discharge coefficient, and p is the water pressure at the leakage point.

[0029] Preferably, in S4, the specific steps are as follows:

[0030] S41: Calculate the maintenance demand decision value MRD of each pipeline based on the risk value and the selected weight group. The calculation method is shown in (4); Based on the risk quantification value R f , combined with the risk value weight ω R and partition weight ω D , calculate the maintenance demand decision value MRD of each pipeline. The specific calculation is shown in formula (4):

[0031] MRD=ω R ×R f +ω D (4)

[0032] Where, MRD is the pipeline maintenance demand decision value; ω R is the risk weight; D is the partition weight. The vital pipeline satisfies ω D =0, the community pipeline satisfies ω R +ω D =1;

[0033] S42: Determine whether, in each community, there is a pipeline MRDmax with the highest MRD value exceeding a given threshold MRD*;

[0034] S43: If the judgment is yes, all communities that exceed the threshold need to repair the corresponding MRDmax pipelines, and the maintenance action and the corresponding pipeline ID are recorded; after the maintenance action occurs, the failure probability and risk value of the maintained pipeline will change. At this time, the updated MRD value of the pipeline needs to be recalculated, and the pipelines that exceed the threshold are maintained in turn, and the cycle continues until there are no more pipelines that exceed the threshold MRD* in the system;

[0035] S44: Arrange the recorded maintenance actions and corresponding pipeline IDs to generate a maintenance demand sequence based on partition weights and dynamic risks; wherein different weight combinations can generate multiple maintenance demand sequences;

[0036] S45: The manager needs to compare and analyze multiple alternative maintenance demand sequences according to his specific needs by comprehensively considering the selected weight group and the WDN performance evaluation results after the execution of each sequence.

[0037] As a preferred embodiment, in S5, in order to obtain the performance evaluation OP of WDN at different stages, it is necessary to first calculate the evaluation weight ω of each node in WDN i And node performance NP, the specific steps are as follows:

[0038] S51: The weight factor represents the importance of the node, using the failure consequence of node i. Indicates the importance of node i; specifically, The cumulative consequences of the failure of m pipes connected to the node The average value of The specific definition of is shown in formula (5):

[0039]

[0040] In the formula, is the failure consequence of node i, and its value range is (0,1]; m is the total number of pipes connected to node i; is the cumulative consequence of the failure of m pipes connected to node i;

[0041] S52: The weight factor of each node i is given by Calculate, where n is the total number of water supply nodes;

[0042] S53: Use the hydraulic simulation solver WNTR open source python package to simulate pipeline leakage and repair, and calculate the water pressure value of the node after considering the leakage or during the gradual repair process;

[0043] S54: When calculating the node performance NP, a pressure-related evaluation model is used; NP is quantified by its ability to meet customer water demand, that is, node satisfaction; an NP value of 1 means that the node fully meets water demand, as shown in formula (6):

[0044]

[0045] In the formula, p i is the actual water pressure at the node, p0 is the predefined lower limit of water pressure, and p u is the upper limit of water pressure;

[0046] S55: According to the NP of each node, the overall WDN performance OP of the WDN is calculated, which is defined as the weighted sum of the NP of each node in the WDN, as shown in formula (7):

[0047]

[0048] In the formula, NP i (t) is the node performance of node i at time t, and its value range is (0,1]; ω i is the weight factor representing the importance of node i; node ω i The weight should be subject to Therefore, the OP range is also [0,1].

[0049] The beneficial effects of the present invention are as follows:

[0050] (1) The present invention takes into account the impact of dynamic risk on WDN repair decisions. The first pipeline to be maintained will affect the hydraulic performance of the remaining pipelines to be maintained. At the same time, the failure probability and risk value of the repaired pipeline will drop to a certain range. At this time, it is necessary to recalculate the updated risk value of the pipeline to determine the next maintenance action, so as to continuously update the maintenance demand sequence and realize dynamic decision-making. At the same time, the optimized dynamic plan can determine the size of the maintenance scale and provide personalized maintenance actions for each pipeline. The results show that compared with the static plan, the optimized dynamic plan can quantify the scale of the specific maintenance actions adopted, so that the performance of the WDN after maintenance is optimized and the overall average risk level of the WDN is reduced.

[0051] (2) The present invention adopts a full life cycle perspective and proposes a decision support method for the WDN system based on dynamic risks to ensure the sustainable operation of the WDN. The method has low data requirements and does not require historical maintenance data of the pipeline network, accurate GIS data, local actual maintenance costs, and customer interruption costs, which greatly reduces data costs. This can improve the universality of the method and make it applicable to newly commissioned WDNs or those that only have current status data. At the same time, the present invention conducted a case study on an actual water supply system and proved that the proposed framework can obtain a maintenance demand sequence based on zoning results and dynamic risk values. Finally, the final long-term maintenance plan is obtained by combining the repair performance score of the WDN and the weight group selected by the manager. It is expected to help managers improve maintenance plans and achieve more effective long-term maintenance planning. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 A flowchart of a dynamic risk-based decision support approach for long-term maintenance of water supply networks;

[0053] Figure 2 This is a schematic diagram of the WDN demand analysis model;

[0054] Figure 3 This is a schematic diagram of pipeline partitioning results;

[0055] Figure 4(a) shows the time-varying brittleness curves of four types of pipes in a clay environment;

[0056] Figure 4(b) shows the time-varying brittleness curves of four types of pipes in a loam environment;

[0057] Figure 4(c) shows the time-varying brittleness curves of four types of pipelines in sandy soil environment;

[0058] Figure 5(a) is a schematic diagram of the failure rate of each pipeline;

[0059] Figure 5(b) is a schematic diagram of the failure consequences of each pipeline;

[0060] Figure 5(c) is a schematic diagram of the risk values ​​of each pipeline;

[0061] Figure 6 It is a schematic diagram of the importance of each node;

[0062] Figure 7 This is a schematic diagram of the OP value trend of WDN;

[0063] Figure 8 This is a schematic diagram of the average failure rate trend of WDN;

[0064] Fig. 9 This is a schematic diagram of the average risk value trend of WDN. DETAILED DESCRIPTION

[0065] In order to further understand the content of the present invention, the present invention is described in detail in conjunction with the accompanying drawings and embodiments. It should be understood that the embodiments are only for explaining the present invention and are not intended to limit it.

[0066] Example

[0067] like Figure 1 As shown, this embodiment provides a dynamic risk-based long-term maintenance decision support method for a water supply network, which includes the following steps:

[0068] S1: Build a data set; the data set includes basic information such as the topological structure of the WDN, the water demand of each node, water supply conditions, the age of each pipeline, pipe material, burial depth, land use and soil type.

[0069] S2: Establish a partition model, use the Girvan-Newman (GN) algorithm to group the pipelines, and after determining the partition results, select a set of weighted values ​​for the relevant partitions as required; the specific steps are as follows:

[0070] S21: Based on the existing WDN graph topology information, the GN algorithm is used to partition and cluster the WDN pipelines. By continuously removing the edges with the largest edge betweenness centrality (EBC) from the network, the remaining pipelines are the community pipelines. EBC is calculated using formula (1):

[0071]

[0072] where EBC(l) = betweenness centrality of edge l; τ s,t (l) = the number of shortest paths between nodes s and t that pass through edge l; τ s,t = the total number of shortest paths from node s to node t; V and E represent the set of nodes and edges respectively;

[0073] S22: Determine the partitioning results and visualize the partitioning effects using the WNTR library and Matplotlib library;

[0074] S23: The manager chooses a set of appropriate weight values ​​ω based on his or her preference, focusing on repairing adjacent community pipelines or repairing vital pipelines with high risk values. D and ω R .

[0075] S3: To quantify the risk of each pipeline, it is necessary to first quantify the failure probability P of the pipeline f and failure consequences C f ; The specific steps are as follows:

[0076] S31: Calculate the failure probability P of the pipeline using the physical probability failure model f ;The failure probability model used considers the relationship between the maximum stress σ on the pipeline and the tensile strength of the pipeline material to calculate the pipeline brittleness curve;

[0077] S32: Calculate the pipeline failure consequence value C using the pipeline failure consequence quantification model f The pipeline failure consequence quantification model used comprehensively analyzes the economic, operational, environmental and social consequences of each pipeline failure based on 14 factors, and then quantifies the overall consequences of each pipeline failure;

[0078] S33: Known failure probability P f and failure consequences C f , then the comprehensive risk R of each pipeline failure can be determined f ; The equation widely used to quantify risk is to multiply the probability of failure by the consequence of failure, as shown in formula (2):

[0079] R f =P f ×C f (2)

[0080] S34: Get the risk value R f After that, we need to calculate the R f Set up a leaky model leak To simplify the model, this embodiment simulates pipeline degradation by setting the flow rate at the leakage point, thus changing the original WDN hydraulic model. The leakage model is shown in formula (3), which introduces the pipeline risk value R f , so that the leakage flow of each pipe will change with the water pressure p and risk value R f Changes occur, as shown in formula (3):

[0081]

[0082] Among them, d leak is the leakage flow, A is the leakage area, C d is the discharge coefficient, and p is the water pressure at the leakage point. Assuming the turbulent discharge coefficient is 0.75, the formula for the leakage area A is A = π × d 2 ×0.2.

[0083] S4: After building a demand analysis module and obtaining multiple maintenance demand sequence plans, the manager will conduct a comparative analysis of the plans based on the needs; the outputs and functions involved in this module are shown in Table 1.

[0084] Table 1 Output information of WDN demand analysis model

[0085]

[0086]

[0087] At the same time, the specific process of this module is as follows Figure 2 , the specific steps are as follows:

[0088] S41: Calculate the maintenance demand decision value (MRD) of each pipeline based on the risk value and the selected weight group. The calculation method is shown in (4). In order to provide a long-term maintenance sequence plan for WDN considering future degradation, this embodiment proposes a method based on the risk quantification value Rf , combined with the risk value weight ω R and partition weight ω D The maintenance demand decision value MRD of each pipeline is calculated by using the method. The pipeline with the largest decision value is given priority for maintenance. The specific calculation is shown in formula (4):

[0089] MRD=ω R ×R f +ω D (4)

[0090] Where, MRD is the pipeline maintenance demand decision value; ω R is the risk weight; D is the partition weight. The vital pipeline (also called a single pipeline) satisfies ω D = 0, the community pipeline (the number of pipelines in the community is not less than 2) satisfies ω R +ω D =1; This embodiment provides several scenarios for changing the weight groups of risk weights and partition weights. Decision makers can accept or reject a maintenance demand sequence according to their own goals, choose to prioritize the maintenance of vital pipelines or community pipelines, and obtain personalized maintenance plans.

[0091] S42: Determine whether there is a pipeline with the highest MRD value (MRDmax) exceeding a given threshold MRD* in each community;

[0092] S43: If the judgment is "yes", all communities that exceed the threshold need to repair the corresponding MRDmax pipelines, and the maintenance action and the corresponding pipeline ID are recorded; after the maintenance action occurs, the failure probability and risk value of the maintained pipeline will change. At this time, the updated MRD value of the pipeline needs to be recalculated, and the pipelines that exceed the threshold are maintained in turn, and the cycle continues until there are no more pipelines that exceed the threshold MRD* in the system;

[0093] S44: Arrange the recorded maintenance actions and corresponding pipeline IDs to generate a maintenance demand sequence based on partition weights and dynamic risks; wherein different weight combinations can generate multiple maintenance demand sequences;

[0094] S45: The manager needs to compare and analyze multiple alternative maintenance demand sequences according to his specific needs by comprehensively considering the selected weight group and the WDN performance evaluation results after the execution of each sequence.

[0095] S5: Establish a performance evaluation model to objectively evaluate the implementation effect of the framework;

[0096] In order to obtain the performance evaluation OP of WDN at different stages, it is necessary to first calculate the evaluation weight ω of each node in WDN iAnd node performance NP, the specific steps are as follows:

[0097] S51: The weight factor represents the importance of the node, using the failure consequence of node i. Indicates the importance of node i; specifically, The cumulative consequences of the failure of m pipes connected to the node The average value of The specific definition of is shown in formula (5):

[0098]

[0099] In the formula, is the failure consequence of node i, and its value range is (0,1]; m is the total number of pipes connected to node i; is the cumulative consequence of the failure of m pipes connected to node i;

[0100] S52: The weight factor of each node i is given by Calculate, where n is the total number of water supply nodes;

[0101] S53: Use the hydraulic simulation solver WNTR open source python package to simulate pipeline leakage and repair, and calculate the water pressure value of the node after considering the leakage or during the gradual repair process;

[0102] S54: When calculating the node performance NP, in order to consider the impact of pipeline leakage, this embodiment adopts a pressure-related evaluation model; NP is quantified by its ability to meet the customer's water demand, that is, node satisfaction; an NP value of 1 indicates that the node fully meets the water demand, as shown in formula (6):

[0103]

[0104] In the formula, p i is the actual water pressure at the node, p0 is the predefined lower limit of water pressure (no water supply), p u is the upper limit of water pressure (the minimum pressure that meets the design water supply demand); in this embodiment, p0 and p u Set to 0 and 30 respectively.

[0105] S55: According to the NP of each node, the overall WDN performance OP of the WDN is calculated, which is defined as the weighted sum of the NP of each node in the WDN, as shown in formula (7):

[0106]

[0107] In the formula, NP i (t) is the node performance of node i at time t, and its value range is (0,1]; ω iis the weight factor representing the importance of node i; node ω i The weight should be subject to Therefore, the OP range is also [0,1]. The weight factor takes into account the relative importance of each node and increases the importance of the key water supply node by assigning more weight to the node.

[0108] S6: Managers need to select the best maintenance sequence from many alternative maintenance requirement sequences to develop a final maintenance plan.

[0109] Experimental process and experimental results

[0110] S1: Dataset Construction

[0111] This embodiment uses the real water supply system research database publicly provided by XXX Institute, and selects the water supply system located in XXX District, namely CA1 system. Detailed information about the system is shown in Table 2 (Table 2 (a), Table 2 (b), Table 2 (c)).

[0112] Table 2 Pipeline maintenance plan for scenario 1

[0113] Table 2 (a) Static solution

[0114]

[0115] Note: 9*: vital pipeline; 123: small-scale maintenance action

[0116] Table 2 (b) Dynamic scheme

[0117]

[0118]

[0119] Note: 9*: vital pipeline; 123: small-scale maintenance action

[0120] Table 2 (c) Optimized dynamic scheme

[0121]

[0122] Note: 9*: vital channel; 123: medium-scale maintenance action; 225: small-scale maintenance action

[0123] The system consists of 111 connection points, 126 pipelines, and 1 elevated water tank. The WDN covers an area of ​​4 square kilometers and has a water pipe length of 17.90 kilometers. The connection points (resident demand nodes) and water sources are defined by nodes, and the pipelines are defined by edges. The Python tool Networkx is used to model the WDN as a directed graph. In addition, most of the system consists of pipes with a diameter of 8 and 12 inches, and a few are 6 and 16 inches.

[0124] This embodiment uses the original topological structure, water demand and water supply conditions of the data set, and uses WNTR to measure the hydraulic performance of WDN. Since the research object is a newly put into use or only has current status data, this type of pipeline network does not have the data required for building a comprehensive degradation model. Therefore, it is necessary to add random simulation data to each pipeline, including factors such as pipeline age, pipe material, burial depth, population density, road accessibility, number of lanes, average traffic volume, land use and soil type. These parameters are randomly generated within a reasonable range. Some data are shown in Table 3.

[0125] Table 3 Partial parameters of pipeline sample data set (10 out of 126 pipelines)

[0126]

[0127] In summary, this embodiment is based on the existing information in the public database and adds simulated data to jointly build this relatively complete data set.

[0128] S2: Partition Module

[0129] S21: Formula (1) is used to calculate the EBC value of each pipeline. After the GN algorithm removes the eight “vital pipelines” with the highest EBC values ​​(pipelines #182, #1542, #2211, #157, #194, #177, #143, and #218) from the WDN, the remaining pipelines are divided into eight communities, named “community pipelines”. The number of communities can be adjusted according to the actual number of maintenance teams.

[0130] S22: In this case, the GN algorithm is used to achieve the effect of WDN partitioning. Figure 3 shown.

[0131] S23: Calculate the pipeline decision priority value ω in formula (4) R and ω D represent the fault risk value and the weight of the WDN partition impact, respectively. When the decision maker is not sure about a specific set of relative weights, it is necessary to obtain the possible range of values ​​of the two weights from the water company managers. Then, the target value of the relative weight group is systematically changed, and ω is weighed and calculated. R and ω D The combination of different weight values ​​can obtain multiple decision scenarios, thus realizing multi-plan decision making. To illustrate the problem, assume that the weight range of risk target is (0.92-0.98) and the weight range of partition target is (0.02-0.08).

[0132] S3: Pipeline Risk Quantification

[0133] Since most water pipes are made of cast iron pipes, it is assumed that the pipe materials in the case are all made of cast iron pipes. In order to be consistent with the pipe properties of the case, this embodiment considers four types of pipes (Type 1: D = 150mm, t = 8mm; Type 2: D = 200mm, t = 10mm; Type 3: D = 300mm, t = 12mm; Type 4: D = 400mm, t = 15mm) for vulnerability analysis. Because most cast iron pipes were produced before 1948, until ductile iron was introduced, the age of the pipe is set to a random number uniformly distributed in the range of 70 to 100 years. Monte Carlo simulation is performed based on 100,000 sampling points to obtain the time-varying failure probability of cast iron pipes. Figure 4 (ac) shows the fragility curves of four different pipes in soil environments of clay, loam and sand, respectively.

[0134] The risk of the WDN pipeline is determined by combining the probability of pipeline failure and the consequences of failure. The specific value of the probability of failure depends on various factors such as the age of the pipe, the wall thickness of the pipe, the operating pressure in the pipe, etc. During the natural deterioration of the pipeline, the growth of the wall corrosion significantly affects the performance of the pipeline. Over time, the thickness of the pipe wall decreases, leading to potential pipeline failure. Since the age of the pipeline is evenly distributed in the range of 70 to 100 years, the minimum age is 70, and the soil is clay, the failure probability of the pipeline in the network needs to be calculated in combination with the fragility curve of Figure 4(b), and the minimum value of the failure probability is about 0.4. The failure rate distribution of each WDN pipeline is shown in Figure 5(a), and Figure 5(b) shows the consequences of failure of each pipeline obtained by fuzzy hierarchical reasoning. Specifically, using the fuzzy hierarchical reasoning system, the comprehensive consequences of each pipeline are calculated in the range of 0-1, and the consequences refer to the potential impact of water pipe failure. Figure 5(c) shows the risk value calculated by the risk equation formula (2). It is calculated that pipeline #123 has the highest risk value of 0.535 because it has a high consequence value of 0.598 and a high failure probability of 0.894. On the other hand, pipeline #226 has a lower risk of 0.170 because it has the lowest consequence value of 0.419 and the lowest failure probability of 0.406. By maintaining pipelines with high risk values, the failure probability of the pipelines can be reduced, thereby reducing the risk value.

[0135] S4: Requirements Analysis Module

[0136] This embodiment uses four decision scenarios for comparative analysis. According to step S23, the corresponding weights of the fault risk value and the partition impact are recommended to be {ω R :0.98,ω D :0.02}, {ω R :0.96,ω D :0.04}, {ω R :0.94,ω D:0.06} and {ω R :0.92,ω D :0.08}. These combinations are obtained based on multiple combination experiments, which can ensure that the pipeline risk value and grouping impact are taken into account while comparing the impact of different weight values ​​on the decision content. Finally, the decision priority value of each pipeline is calculated using formula (4).

[0137] The solution that can be directly obtained by comparing the MRD value and MRD* of each pipeline, that is, the maintenance solution that does not consider the dynamic change of the risk value, is called a static solution. R :0.98,ω D :0.02) as an example, because the pipeline is relatively old, it can be found from Table 2(a) that a total of 87 pipelines need to be repaired. The MRD values ​​of these pipelines exceed MRD*, and the same maintenance work is performed in order from large to small according to their MRD values. In fact, during the pipeline repair process, its risk value will change dynamically with the maintenance action. Assuming that the pipeline is repaired to the same degree each time during the maintenance process, the age of each pipeline will be reduced by 20 years (the minimum age is 1). Then recalculate the pipeline degradation rate and pipeline risk value, and then update the next maintenance action, and finally update the maintenance plan. Table 2(b) is a maintenance plan that takes into account the dynamic change of risk value, that is, a dynamic plan. The MRD value of some pipelines is so large that two maintenance projects are required to ensure that their MRD values ​​remain below MRD*, such as the #130 pipeline and the #144 pipeline in community 3. This plan requires a total of 113 maintenance actions. In actual maintenance work, each pipeline is only excavated once, and it is not realistic to perform maintenance according to the pipeline maintenance sequence in the plan in Table 2(b). Therefore, the pipelines that have been maintained more than once are recorded. If the pipeline appears twice in the plan, a medium maintenance action is performed, and if it appears three times, a major maintenance action is performed. A maintenance operation is performed once when it appears for the first time in the plan. The optimized dynamic plan is shown in Table 2(c). The table shows that the plan requires a total of 90 pipelines to be repaired, including 23 medium maintenance and 67 minor maintenance. Therefore, the dynamic plan can more specifically determine whether each pipeline needs major maintenance, medium maintenance or minor maintenance, and provide more accurate maintenance actions according to the pipeline conditions.

[0138] S5: WDN Performance Evaluation

[0139] According to the topological structure of WDN, the node importance is calculated by formula (7) to obtain the node weight ω of the WDN evaluation index: i , the value is Figure 6 As shown. Taking scenario 1 (ω R :0.98,ω D:0.02) as an example (the same applies to other scenarios), the specific maintenance plan is shown in Table 2. The hydraulic performance after pipeline degradation is considered through WNTR simulation, and the initial OP value of WDN before repair is calculated according to formula (6) to be approximately 0.69166. The maintenance team of each community starts to repair the pipeline with the highest MRD value in the corresponding community at the same time. One time step corresponds to the simultaneous repair of the first pipeline in each community. And after each maintenance action of a time step is completed, WNTR is used to simulate the overall hydraulic performance OP value of the gradually maintained WDN. Table 2 lists the specific contents of the three schemes: static scheme, dynamic scheme, and optimized dynamic scheme. At the same time, their corresponding OP value change trends during the maintenance process of never considering degradation, considering degradation, and each step are as follows Figure 7 As shown. It can be found that after executing the static solution, the OP value at the end of maintenance is the lowest, which is 0.79363, which is 14.74% higher than the initial OP value. After executing the two dynamic solutions, the OP values ​​both reached 0.82543, which is 19.34% higher than the initial OP value, and 4.60% higher than the static solution. In addition, since the solution only chooses to repair pipelines with MRD values ​​greater than MRD*, the OP value cannot return to 1 after maintenance, but returns to the daily operation and maintenance of the pipeline, reducing the safety range of the probability of risk accidents. At the same time, the average failure rate change trends of the three solutions are shown as follows: Figure 8 As shown. It can be found that after the static solution is implemented, the average failure rate at the end of maintenance is the highest, which is 0.56543, which is 20.05% lower than the initial average failure rate of 0.70726. After the two dynamic solutions are implemented, the average failure rate is reduced to 0.52038, which is 26.42% lower than the initial average failure rate and 6.37% lower than the static solution. In addition, the average risk value change trend of the three solutions is as follows Fig. 9 As shown. It can be found that after executing the static solution, the average risk value at the end of maintenance is the highest, which is 0.26386, which is 21.44% lower than the initial average risk value of 0.33587. After executing the two dynamic solutions, the average risk value dropped to 0.23752, which is 29.28% lower than the initial average risk value, and 7.84% lower than the static solution. Among them, the optimized dynamic solution has a time step reduction of 6 compared to the unoptimized dynamic solution, which is the minimum value of 27 among the three solutions. In other words, the optimized dynamic solution can make the WDN performance reach the optimal fastest and make the WDN average risk value reach the lowest fastest. Therefore, this embodiment selects the optimized dynamic solution to assist decision-making.

[0140] S6: The manager comprehensively compares the analysis results of the four scenarios, combines their own needs, and selects the final maintenance plan from many alternative maintenance demand sequences.

[0141] This paper considers the impact of pipeline zoning and dynamic risk changes on WDN maintenance decisions, and proposes a WDN long-term maintenance decision support framework based on dynamic risks. At the same time, the framework is applied through cases to illustrate how the method specifically makes long-term maintenance decisions for newly commissioned pipelines or pipelines with only current status data, and evaluates the hydraulic performance of WDN at different stages. The new framework proposed in this paper is combined with case analysis and found that in scenario 1 (ω R :0.98,ω D :0.02), after the optimized dynamic scheme is fully executed, the following effects can be achieved relative to the static scheme: (1) The overall performance of WDN is improved by 19.34% relative to the initial value, which is 4.60% more than the static scheme; (2) The average failure probability is reduced by 26.42% relative to the initial value, which is 6.37% more than the static scheme; (3) The average risk value is reduced by 29.28% relative to the initial value, which is 7.84% more than the static scheme. Therefore, the present invention is expected to provide a more accurate and practical theoretical basis for risk-oriented pipeline maintenance decisions, help water management personnel make daily WDN maintenance decisions, and achieve effective long-term maintenance planning.

[0142] The present invention and its embodiments are described schematically above, and the description is not restrictive. The drawings show only one embodiment of the present invention, and the actual structure is not limited thereto. Therefore, if a person skilled in the art is inspired by it and designs a structural method and an embodiment similar to the technical solution without creativity without departing from the purpose of the invention, they shall all fall within the protection scope of the present invention.

Claims

1. A dynamic risk-based long-term maintenance decision support method for water supply networks, characterized by: The following steps are involved: S1: Build the dataset; S2: Establish a partition model, use the GN algorithm to group the pipelines, and after determining the partition results, select a set of weight groups for the relevant partitions as required; In S2, the specific steps are as follows: S21: Based on the existing WDN graph topology information, the GN algorithm is used to partition and cluster the WDN pipelines. By continuously removing the edges with the largest edge betweenness centrality EBC from the network, the remaining pipelines are the community pipelines. EBC is calculated using formula (1): where EBC(l) = betweenness centrality of edge l; τ s,t (l) = the number of shortest paths between nodes s and t that pass through edge l; τ s,t = the total number of shortest paths from node s to node t; V and E represent the set of nodes and edges respectively; S22: Determine the partitioning results and visualize the partitioning effects using the WNTR library and Matplotlib library; S23: The manager chooses a set of appropriate weight values ​​ω based on his or her preference, focusing on repairing adjacent community pipelines or repairing vital pipelines with high risk values. D and ω R ; S3: To quantify the risk of each pipeline, it is necessary to first quantify the failure probability P of the pipeline f and failure consequences C f ; In S3, the specific steps are as follows: S31: Calculate the failure probability P of the pipeline using the physical probability failure model f ;The failure probability model used considers the relationship between the maximum stress σ on the pipeline and the tensile strength of the pipeline material to calculate the pipeline brittleness curve; S32: Calculate the pipeline failure consequence value C using the pipeline failure consequence quantification model f The pipeline failure consequence quantification model used comprehensively analyzes the economic, operational, environmental and social consequences of each pipeline failure based on 14 factors, and then quantifies the overall consequences of each pipeline failure; S33: Known failure probability P f and failure consequences C f , then the comprehensive risk R of each pipeline failure can be determined f ; The equation widely used to quantify risk is to multiply the probability of failure by the consequence of failure, as shown in formula (2): R f =P f ×C f (2) S34: Get the risk value R f After that, we need to calculate the R f Set up a leaky model leak The leakage model is shown in formula (3), which introduces the risk value R of the pipeline f , so that the leakage flow of each pipe will change with the water pressure p and risk value R f Changes occur, as shown in formula (3): Among them, d leak is the leakage flow, A is the leakage area, C d is the discharge coefficient, p is the water pressure at the leakage point; S4: After building a demand analysis module and obtaining multiple maintenance demand sequence plans, the management personnel conduct comparative analysis of the plans based on the needs; In S4, the specific steps are as follows: S41: Calculate the maintenance demand decision value MRD of each pipeline based on the risk value and the selected weight group. The calculation method is shown in (4); Based on the risk quantification value R f , combined with the risk value weight ω R and partition weight ω D , calculate the maintenance demand decision value MRD of each pipeline. The specific calculation is shown in formula (4): MRD=ω R ×R f +ω D (4) Where, MRD is the pipeline maintenance demand decision value; ω R is the risk weight; D is the partition weight; the vital pipeline satisfies ω D =0, the community pipeline satisfies ω R +ω D =1; S42: Determine whether, in each community, there is a pipeline MRDmax with the highest MRD value exceeding a given threshold MRD*; S43: If the judgment is yes, all communities that exceed the threshold need to repair the corresponding MRDmax pipelines, and the maintenance action and the corresponding pipeline ID are recorded; after the maintenance action occurs, the failure probability and risk value of the maintained pipeline will change. At this time, the updated MRD value of the pipeline needs to be recalculated, and the pipelines that exceed the threshold are maintained in turn, and the cycle continues until there are no more pipelines that exceed the threshold MRD* in the system; S44: Arrange the recorded maintenance actions and corresponding pipeline IDs to generate a maintenance demand sequence based on partition weights and dynamic risks; wherein different weight combinations can generate multiple maintenance demand sequences; S45: The manager needs to compare and analyze multiple alternative maintenance demand sequences according to their specific needs by comprehensively considering the selected weight group and the WDN performance evaluation results after each sequence is executed; S5: Establish a performance evaluation model to objectively evaluate the implementation effect; S6: Managers need to select the best maintenance sequence from many alternative maintenance requirement sequences to develop a final maintenance plan.

2. The method for long-term maintenance decision support of a water supply network based on dynamic risk according to claim 1, characterized in that: In S1, the dataset includes the topological structure of WDN, water demand of each node, water supply conditions, age of each pipeline, pipe material, burial depth, land use and soil type.

3. The method for long-term maintenance decision support of a water supply network based on dynamic risk according to claim 2, characterized in that: In S5, in order to obtain the performance evaluation OP of WDN at different stages, it is necessary to first calculate the evaluation weight ω of each node in WDN i And node performance NP, the specific steps are as follows: S51: The weight factor represents the importance of the node, using the failure consequence of node i. Indicates the importance of node i; specifically, The cumulative consequences of the failure of m pipes connected to the node The average value of The specific definition of is shown in formula (5): In the formula, is the failure consequence of node i, and its value range is (0,1]; m is the total number of pipelines connected to node i; is the cumulative consequence of the failure of m pipes connected to node i; S52: The weight factor of each node i is given by Calculate, where n is the total number of water supply nodes; S53: Use the hydraulic simulation solver WNTR open source python package to simulate pipeline leakage and repair, and calculate the water pressure value of the node considering the leakage or gradual repair process; S54: When calculating the node performance NP, a pressure-related evaluation model is used; NP is quantified by its ability to meet customer water demand, that is, node satisfaction; an NP value of 1 means that the node fully meets water demand, as shown in formula (6): In the formula, p i is the actual water pressure at the node, p0 is the predefined lower limit of water pressure, and p u is the upper limit of water pressure; S55: According to the NP of each node, the overall WDN performance OP of the WDN is calculated, which is defined as the weighted sum of the NP of each node in the WDN, as shown in formula (7): In the formula, NP i (t) is the node performance of node i at time t, and its value range is (0,1]; ω i is the weight factor representing the importance of node i; node ω i The weight should be subject to Therefore, the OP range is also [0,1].

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