A multi-objective optimization arrangement method and system for a water supply network pressurizing pump station based on peak-time sensitive toughness

Abstract

The present application relates to water supply network technical field, disclose a kind of based on peak time sensitive toughness water supply network pressurizing pump station multi-objective optimization arrangement method and system, the method includes: constructing hydraulic model to carry out time-varying simulation, identify weak node of pressure;According to the deviation of each time period water demand and average water demand, peak time sensitive toughness index is obtained by weighted calculation of system toughness index, so that higher weight is obtained in peak period;Hydraulic disturbance is exerted to potential node, and candidate node is screened according to the pressure improvement degree of weak node;Multi-objective optimization model is constructed with the index as optimization target, with candidate node site discrete variable and scale continuous variable as decision variable;Non-dominated solution set is obtained by using multi-objective evolutionary solution strategy, and arrangement scheme is output by multi-attribute decision sorting.This application focuses on peak period by peak time sensitive weighting, and corrects the deviation that traditional toughness index may prefer to improve low peak period and tolerate high peak deterioration due to averaging.

Description

Technical Field

[0001] This invention relates to the field of water supply network technology, specifically to a multi-objective optimization layout method and system for booster pump stations in water supply networks based on peak-hour sensitive resilience. Background Technology

[0002] Urban water supply networks are critical infrastructure for ensuring the smooth operation of society. With rapid urbanization, some areas, due to their distance from water treatment plants, high altitude, or insufficient network capacity, face water supply bottlenecks characterized by low pressure under normal conditions, which worsens during peak hours. Compared to traditional scenarios that only focus on insufficient peak pressure, the problem of low pressure under normal conditions and worsening pressure during peak hours significantly increases the number of vulnerable nodes and areas requiring attention within the network, raising the optimization requirements considerably and making the problem extremely complex. To alleviate these pressure bottlenecks, appropriately adding booster pump stations to the network is an important engineering measure; however, the selection of their location and scale directly affects the project's economic viability and the system's water supply security.

[0003] Currently, research on the optimization of water supply networks mainly focuses on economic scheduling or performance improvement based on reliability. In terms of resilience assessment, existing technologies typically use the traditional Modified Resilience Index (MRI) or its demand-weighted form (IMRI) as evaluation indicators of system performance. Using this as the objective, multi-objective evolutionary algorithms such as the Non-Dominated Sorting Genetic Algorithm (NSGA-II) based on traditional genetic algorithms are combined to optimize the location and capacity of booster pump stations. These conventional indicators characterize the overall service level of the network in response to time-varying loads by calculating the mean or proportion of the system's remaining energy over different time periods.

[0004] However, on the one hand, existing resilience assessment indicators uniformize the performance across different time periods, which is insufficient to characterize the vulnerability during peak periods under normal low pressure and peak exacerbation scenarios. This leads to the optimization of booster pump station layouts deviating from the core engineering requirements of ensuring peak water supply. On the other hand, existing solution methods such as NSGA-II have weak constraint handling capabilities and low search efficiency when facing high-dimensional and complex constraint solution scenarios brought about by normal low pressure and peak exacerbation problems, making it difficult to quickly find the optimal solution in the vast solution space. Summary of the Invention

[0005] This invention provides a multi-objective optimization layout method and system for booster pump stations in water supply networks based on peak-time sensitive resilience, in order to solve the problem that the optimization layout of existing booster pump stations deviates from the core engineering requirements of ensuring peak water supply.

[0006] In a first aspect, the present invention provides a multi-objective optimization layout method for booster pump stations in a water supply network based on peak-time sensitive resilience, the method comprising: A hydraulic model is constructed based on the basic parameters of the target water supply network, and a time-varying hydraulic simulation is performed to identify weak nodes in the network where the pressure is lower than a preset pressure threshold during normal periods and during peak periods. Extract the system resilience index for each time period from the time-varying hydraulic simulation results, and calculate the system resilience index by weighting it according to the deviation between the system water demand for each time period and the average water demand of the periodic system, to obtain the peak-time sensitive resilience index. Hydraulic disturbances are applied to preset potential nodes, and candidate nodes are selected from the potential nodes based on the degree of pressure improvement of the weak nodes after the disturbance. Construct a multi-objective optimization model; the multi-objective optimization model takes at least the peak time sensitivity resilience index as the optimization objective, and the discrete variables of the candidate node's location and the continuous variables of its size as decision variables; A multi-objective evolutionary solution strategy is used to solve the multi-objective optimization model to obtain a non-dominated solution set; The non-dominated solution set is sorted by multi-attribute decision to obtain the pressurization facility layout scheme of the target water supply network.

[0007] In one optional implementation, the step of weighting the system resilience index based on the deviation between the system water demand in each time period and the average water demand of the system over a period of time to obtain a peak-time sensitive resilience index includes: Calculate the ratio of the system's water demand in each time period to the system's average water demand over the period; The ratio is nonlinearly mapped to generate peak sensitivity coefficients for each time period; the peak sensitivity coefficient for the time period when the system water demand is greater than the average water demand of the periodic system is greater than 1. The system resilience index for each time period is obtained by taking the product of the system water demand for each time period and the peak sensitivity coefficient as a comprehensive weight and averaging the index for each time period.

[0008] In one optional implementation, the step of applying hydraulic disturbance to preset potential nodes and selecting candidate nodes from the potential nodes based on the degree of pressure improvement of the weak nodes after the disturbance includes: At each of the preset potential nodes, a virtual head increment of a preset amplitude is applied, and the time-varying hydraulic simulation is re-executed to obtain the updated pressure value of each of the weak nodes. Calculate the weighted sum of the pressure improvement amount of each weak node before and after the perturbation is applied to each potential node, and use it as the pressure improvement degree of the corresponding potential node; Potential nodes whose pressure improvement is below a preset improvement threshold are removed, and the remaining potential nodes are selected as candidate nodes.

[0009] In one optional implementation, the optimization objectives of the multi-objective optimization model further include minimizing the economic cost of construction and operation and maximizing the overall reliability of the system; The constraints of the multi-objective optimization model include the lower limit constraint of node pressure, the pump flow rate constraint, and the pipe section flow velocity constraint.

[0010] In one optional implementation, the step of solving the multi-objective optimization model using a multi-objective evolutionary solution strategy includes: The discrete variables for the location of the candidate nodes are encoded using binary encoding, and the continuous variables for scale are encoded using real numbers to generate an initial population with mixed encoding. Based on the initial population, an evolutionary iteration is performed. In each generation of the evolutionary iteration process, the step size factor is calculated according to the hierarchical mechanism of the gray wolf optimization algorithm. The position of the continuous variables is directly updated, and the discrete variables are updated collaboratively through the transfer function to generate the offspring population.

[0011] In one alternative implementation, in each generation of the evolutionary iteration process, the feasible solution file and the near-feasible solution file are dynamically updated for dual-file guidance; the feasible solution file stores solutions that satisfy all constraints, and the near-feasible solution file stores solutions with constraint violation degrees less than a dynamic threshold; Based on the feasible solution file, a preset number of elite solutions are extracted, and a covariance matrix is ​​constructed using the local statistical distribution of the elite solutions; Based on the covariance matrix, local covariance learning is performed to generate new individual solutions that satisfy the constraints of the multi-objective optimization model.

[0012] In one alternative implementation, when updating the feasible solution file and the near-feasible solution file, an extreme point retention strategy is performed to retain the non-dominated solutions concentrated at the boundary positions in each optimization objective direction.

[0013] In one optional implementation, the multi-attribute decision ranking of the non-dominated solution set includes: The weight vectors of each optimization objective are determined based on preset decision preferences; the decision preferences include cost preference, equilibrium preference, or performance preference. Based on the weight vector, each optimization objective is normalized and weighted, and the distance between each solution and the positive ideal solution and the negative ideal solution is calculated to obtain the relative fitting progress. Sort the solutions in descending order of relative application progress and output the sorted list.

[0014] Secondly, the present invention provides a multi-objective optimization layout system for booster pump stations in a water supply network based on peak-time sensitive resilience, the system comprising: The data acquisition and simulation module is used to construct a hydraulic model based on the basic parameters of the target water supply network and perform time-varying hydraulic simulation to identify weak nodes in the network where the pressure is lower than a preset pressure threshold during normal periods and during peak periods. The resilience assessment module is used to extract the system resilience index for each time period in the time-varying hydraulic simulation results, and to perform weighted calculation on the system resilience index based on the deviation between the system water demand for each time period and the average water demand of the periodic system to obtain the peak-time sensitive resilience index. The candidate node screening module is used to apply hydraulic disturbance to a preset potential node and screen candidate nodes from the potential nodes based on the degree of pressure improvement of the weak node after the disturbance. An optimization solution engine module is used to construct a multi-objective optimization model and to solve the multi-objective optimization model using a multi-objective evolutionary solution strategy to obtain a non-dominated solution set; the multi-objective optimization model takes at least the peak-time sensitivity resilience index as the optimization objective and the discrete location variables and continuous scale variables of the candidate nodes as decision variables; The decision support module is used to perform multi-attribute decision ranking on the non-dominated solution set to obtain the pressurization facility layout scheme of the target water supply network.

[0015] Thirdly, the present invention provides an electronic device, comprising: a memory and a processor, wherein the memory and the processor are communicatively connected to each other, the memory stores computer instructions, and the processor executes the computer instructions to perform a multi-objective optimization layout method for booster pump stations of water supply networks based on peak-time sensitive resilience as described in the first aspect or any corresponding embodiment.

[0016] Fourthly, the present invention provides a computer-readable storage medium storing computer instructions for causing a computer to execute a multi-objective optimization layout method for booster pump stations in a water supply network based on peak-time sensitive resilience, as described in the first aspect above or any corresponding embodiment.

[0017] Fifthly, the present invention provides a computer program product, including computer instructions, which are used to cause a computer to execute a multi-objective optimization layout method for booster pump stations in a water supply network based on peak-time sensitive resilience as described in the first aspect above or any corresponding embodiment.

[0018] This invention first identifies weak points in the pipeline network during normal and peak periods through time-varying hydraulic simulation. Addressing the increased optimization dimensionality caused by normal low pressure and peak-period deterioration, it provides a clear target area for subsequent optimization. Secondly, addressing the shortcomings of existing resilience indices that uniformly treat performance across time periods and fail to accurately characterize system performance under the combined effects of normal low pressure and peak-period deterioration, this invention proposes a resilience assessment method incorporating a peak-period sensitivity coefficient. This method weights the system resilience index based on the deviation between water demand in each time period and the cyclical average water demand, giving higher weight to peak periods with higher water demand. This proactively focuses optimization efforts on peak periods, correcting the bias that might arise from index averaging, which could prioritize improving low-peak periods and tolerate peak-period deterioration. Building upon this foundation, by applying hydraulic disturbances to potential nodes and selecting candidate nodes based on the degree of pressure improvement at weak nodes, the scale of decision variables is effectively reduced. Furthermore, a multi-objective optimization model is constructed, with peak-time sensitivity resilience as the optimization objective and discrete location and continuous scale as decision variables. To improve the model's performance under complex constraints, an improved multi-objective gray wolf optimization algorithm is employed. Through mixed variable collaborative updates, dual-file guidance, local covariance learning, and extreme point retention strategies, a non-dominated solution set is obtained. Finally, a layout scheme matching engineering preferences is output after multi-attribute decision ranking. These interconnected steps provide a quantitative, efficient, and balanced decision-making basis for the optimized layout of booster pump stations in water supply networks, ensuring water supply security during both normal and peak periods. Attached Figure Description

[0019] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0020] Figure 1 This is a schematic diagram of an application scenario according to an embodiment of the present invention; Figure 2 This is a first flowchart of a multi-objective optimization layout method for booster pump stations in a water supply network based on peak-time sensitive resilience, according to an embodiment of the present invention. Figure 3 This is a second flowchart of a multi-objective optimization layout method for booster pump stations in a water supply network based on peak-time sensitive resilience, according to an embodiment of the present invention. Figure 4 This is a third flowchart of a multi-objective optimization layout method for booster pump stations in a water supply network based on peak-time sensitive resilience, according to an embodiment of the present invention. Figure 5This is a schematic diagram illustrating the calculation principle of the peak-time sensitive integrated toughness index (PIMRI) according to an embodiment of the present invention; Figure 6 This is a flowchart of the improved multi-objective gray wolf optimization algorithm (CAMOGWO-FN) according to an embodiment of the present invention; Figure 7 This is a schematic diagram of the dual-file guidance mechanism of the improved multi-objective gray wolf optimization algorithm (CAMOGWO-FN) according to an embodiment of the present invention; Figure 8 This is a schematic diagram of the local covariance learning mechanism of the improved multi-objective gray wolf optimization algorithm (CAMOGWO-FN) according to an embodiment of the present invention; Figure 9 This is a schematic diagram of the hybrid variable update and repair mechanism of the improved multi-objective gray wolf optimization algorithm (CAMOGWO-FN) according to an embodiment of the present invention; Figure 10 This is a comparison chart of the contributions of PIMRI and traditional indicators (IMRI) to the resilience index at different time periods according to an embodiment of the present invention; Figure 11 This is a schematic diagram comparing the total cost with the frontier of the PRsys objective function algorithm according to an embodiment of the present invention; Figure 12 This is a schematic diagram comparing the total cost with the frontier of the PIMRI objective function algorithm according to an embodiment of the present invention; Figure 13 This is a schematic diagram of the distribution of candidate pressurization nodes in a central urban area of ​​a city according to an embodiment of the present invention; Figure 14 This is a performance comparison chart of the top three schemes obtained by TOPSIS ranking under different decision preferences according to an embodiment of the present invention; Figure 15 This is a structural block diagram of a multi-objective optimization layout system for a water supply network booster pump station based on peak-time sensitive resilience, according to an embodiment of the present invention. Figure 16 This is a schematic diagram of the hardware structure of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] It is understood that before using the technical solutions disclosed in the various embodiments of the present invention, users should be informed of the types, scope of use, and usage scenarios of the personal information involved in the present invention and their authorization should be obtained in accordance with relevant laws and regulations through appropriate means.

[0023] As an optional application scenario of this invention, such as Figure 1 As shown, the system may include at least one terminal device and at least one server. Figure 1 The system is illustrated in the example, which includes a computer 101, a mobile terminal 102, and a server 103, and the terminal devices such as the computer 101 and the mobile terminal 102 are connected to the server 103 through a network 110.

[0024] Computer 101 can be a desktop computer belonging to a water supply company or municipal planning and design department, used by engineers to upload basic pipeline data, set optimization parameters, and view detailed plan reports. Mobile terminal 102 can be a smartphone or tablet, used by on-site inspection personnel to receive candidate node locations, weak node distributions, and final recommended solutions pushed by the server, for verification and confirmation during on-site inspections. Server 103 can be a standalone physical server, cloud server, or server cluster, equipped with a processor, memory, storage devices, and input / output interfaces, and installed with a hydraulic simulation engine (such as EPANET 2.2) and an optimization algorithm programming platform (such as Python or MATLAB).

[0025] Engineers upload basic data of the target water supply network (including node elevation, pipe segment parameters, water usage patterns, cost parameters, etc.) to a client on computer 101. The data is transmitted to server 103 via network 110. Server 103 calls a hydraulic model to perform time-varying simulations to identify pressure-vulnerable nodes; calculates peak-hour sensitivity resilience indices based on the deviation between water demand in each time period and the periodic average water demand; applies virtual hydraulic disturbances to potential nodes and selects candidate nodes based on the degree of pressure improvement of weak nodes; constructs a multi-objective optimization model with full life-cycle cost, system periodic reliability, and peak-hour sensitivity resilience indices as optimization objectives; iteratively solves the problem using an improved multi-objective evolutionary solution strategy to obtain a non-dominated solution set; finally, it generates a recommended booster pump station scheme through multi-attribute decision ranking. Server 103 returns the calculation results to computer 101, displaying detailed schemes in the form of charts and lists. Simultaneously, server 103 can push information such as candidate node locations and weak area distribution to mobile terminal 102 for field verification by on-site personnel. Engineers combine indoor analysis and on-site verification results to select the final implementation scheme.

[0026] According to an embodiment of the present invention, a method for multi-objective optimization of the layout of booster pump stations in a water supply network based on peak-time sensitive resilience is provided. It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions. Furthermore, although a logical order is shown in the flowchart, in some cases, the steps shown or described may be executed in a different order than that shown here.

[0027] This embodiment provides a multi-objective optimization layout method for booster pump stations in water supply networks based on peak-time sensitive resilience, which can be used in the aforementioned server 103. Figure 2 This is a first flowchart of a multi-objective optimization layout method for booster pump stations in a water supply network based on peak-time sensitive resilience, according to an embodiment of the present invention. Figure 2 As shown, the process includes the following steps: Step S201: Construct a hydraulic model based on the basic parameters of the target water supply network and perform time-varying hydraulic simulation to identify weak nodes in the network where the pressure is lower than a preset pressure threshold during normal periods and during peak periods.

[0028] Furthermore, this step first collects basic parameters of the target water supply network, including pipe diameter, length, roughness coefficient, and ground elevation and spatial topology of nodes, to construct a hydraulic model reflecting the actual physical connections in the software. Subsequently, time-varying hydraulic simulation is performed, incorporating user water demand data fluctuating over a 24-hour period to calculate the hydraulic state of the network under various load conditions. Addressing the issue of low pressure during normal periods and worsening pressure during peak periods, by comparing the calculated pressure of nodes at different times with the preset minimum service pressure threshold, nodes with substandard pressure during both normal and high-load peak periods can be comprehensively identified and marked as weak nodes. This step overcomes the shortcomings of traditional steady-state analysis, which cannot reflect dynamic fluctuations and struggles to simultaneously account for both normal and peak pressures, providing accurate spatial targets for the subsequent targeted deployment of pressurization facilities.

[0029] Step S202: Extract the system resilience index for each time period from the time-varying hydraulic simulation results, and calculate the system resilience index by weighting according to the deviation between the system water demand for each time period and the average water demand of the periodic system, to obtain the peak-time sensitive resilience index.

[0030] Furthermore, the system resilience index is a technical indicator used to measure the ability of a pipeline network to maintain normal water supply capacity when faced with internal load fluctuations or external disturbances. In time-varying simulation results, the pipeline network exhibits different resilience levels at different times. This step quantifies the load characteristics of each time period by calculating the deviation between the system water demand for each time period and the average water demand throughout the day. Based on this deviation, the resilience index for each time period is calculated with differentiated weighting: when the water demand for a certain time period is significantly higher than the average (i.e., peak period), it is given a higher calculation weight; conversely, the weight is reduced. After this weighted fusion, a comprehensive peak-sensitive resilience index is obtained. This index changes the previous calculation method of equal weighting for all time periods throughout the day, making the evaluation results more sensitive to peak water supply conditions, thus truly reflecting the operational resilience of the pipeline network under the most critical operating conditions at a macro level.

[0031] Step S203: Apply hydraulic disturbance to the preset potential node, and select candidate nodes from the potential nodes based on the degree of pressure improvement of the weak node after the disturbance.

[0032] Furthermore, in this embodiment, a batch of potential nodes are pre-defined in the pipeline network topology, i.e., locations where booster pump stations can be built based on engineering experience or geographical conditions. Next, hydraulic disturbances are applied to these potential nodes, i.e., a certain water pressure (such as a virtual head) is virtually increased for these nodes in the mathematical model to simulate the hydraulic response of the pipeline network after pressurization. By comparing the pressure changes of the weak nodes identified in step S201 before and after the disturbance, the contribution of each potential node to improving the low-pressure situation of the pipeline network, i.e., the degree of pressure improvement, is quantified. If the pressure in the weak area of ​​a potential node hardly increases after the disturbance is applied, it indicates that the geographical location is poor or hydraulic conduction is obstructed. Therefore, by setting a reasonable threshold, nodes with low improvement levels are eliminated, and only potential nodes that can effectively improve the pipeline network pressure are retained as candidate nodes, thereby effectively reducing the space for subsequent optimization search.

[0033] Step S204: Construct a multi-objective optimization model; the multi-objective optimization model takes at least the peak-time sensitivity resilience index as the optimization objective and the discrete variables of the candidate node's location and the continuous variables of its size as decision variables.

[0034] Furthermore, a multi-objective optimization model is a mathematical framework capable of simultaneously handling multiple mutually constraining optimization objectives. In this embodiment, the core optimization objective of the multi-objective optimization model includes at least the peak-time sensitivity resilience index calculated in step S202 (pursuing maximum resilience). Additionally, depending on actual engineering needs, other objectives such as economic cost (pursuing minimum cost) are often introduced. To achieve these objectives, the multi-objective optimization model needs to define decision variables, i.e., the means that engineers can adjust. These decision variables are divided into two categories: one is discrete location variables, representing whether or not to build pressurization facilities among the candidate nodes selected in step S203, which are logical choices of either 0 or 1; the other is continuous scale variables, representing the specific water supply scale or pump parameters if pressurization facilities are built, which can continuously take values ​​within a certain range. By clarifying the mathematical relationship and constraints between the objectives and variables, the optimization model is constructed.

[0035] Step S205: The multi-objective evolutionary solution strategy is used to solve the multi-objective optimization model to obtain the non-dominated solution set.

[0036] Furthermore, since the aforementioned multi-objective optimization model contains both discrete and continuous decision variables, and there are often conflicts between multiple optimization objectives (for example, improving resilience often requires increasing construction costs), traditional analytical methods are difficult to solve directly. Therefore, this embodiment adopts a multi-objective evolutionary solution strategy, which is a heuristic search algorithm inspired by biological natural selection and genetic mechanisms. It generates an initial group of solutions and uses selection, crossover, and mutation operations during the iteration process to continuously evolve the group towards a better direction. After multiple generations of evolution, the algorithm converges and outputs a non-dominated solution set. In this solution set, any solution is better than any other solution in the set in at least one objective and worse in another; there is no absolutely globally optimal solution.

[0037] Step S206: Perform multi-attribute decision sorting on the non-dominated solution set to obtain the pressurization facility layout scheme for the target water supply network.

[0038] Furthermore, while non-dominated solution sets offer a wealth of choices, engineering implementation often requires adopting only one specific solution. Multi-attribute decision ranking is an auxiliary decision-making technique that allows assigning different preference weights to various optimization objectives based on the specific project's focus. Based on these weights, the performance of each solution in the non-dominated solution set across different objectives is comprehensively and quantitatively calculated, resulting in a comprehensive score or proximity index. Finally, all solutions are ranked from highest to lowest according to this index, with the top-ranked solution being the one with the best overall performance. This clearly outputs a target water supply network pressurization facility layout scheme that includes specific pressurization facility location and construction scale, guiding actual engineering construction.

[0039] In summary, this invention first identifies weak points in the pipeline network during normal and peak periods through time-varying hydraulic simulation. Addressing the increased optimization dimensionality caused by normal low pressure and peak-period deterioration, it provides a clear target area for subsequent optimization. Secondly, addressing the shortcomings of existing resilience indices that uniformly process performance across time periods and fail to accurately characterize system performance under the combined effects of normal low pressure and peak-period deterioration, this invention proposes a resilience assessment method incorporating a peak-period sensitivity coefficient. This method weights the system resilience index based on the deviation between water demand in each time period and the cyclical average water demand, giving higher weight to peak periods with higher water demand. This proactively focuses optimization efforts on peak periods, correcting the bias that might arise from index averaging, which could prioritize improving low-peak periods and tolerate peak-period deterioration. Building upon this foundation, by applying hydraulic disturbances to potential nodes and selecting candidate nodes based on the degree of pressure improvement at weak nodes, the scale of decision variables is effectively reduced. Furthermore, a multi-objective optimization model is constructed, with peak-time sensitivity resilience as the optimization objective and discrete location and continuous scale as decision variables. To improve the model's performance under complex constraints, an improved multi-objective gray wolf optimization algorithm is employed. Through mixed variable collaborative updates, dual-file guidance, local covariance learning, and extreme point retention strategies, a non-dominated solution set is obtained. Finally, a layout scheme matching engineering preferences is output after multi-attribute decision ranking. These interconnected steps provide a quantitative, efficient, and balanced decision-making basis for the optimized layout of booster pump stations in water supply networks, ensuring water supply security during both normal and peak periods.

[0040] Figure 3 This is a second flowchart of a multi-objective optimization layout method for booster pump stations in a water supply network based on peak-time sensitive resilience, according to an embodiment of the present invention. Figure 3 As shown, the process includes the following steps: Step S301: Construct a hydraulic model based on the basic parameters of the target water supply network and perform time-varying hydraulic simulation to identify weak nodes in the network where the pressure is lower than a preset pressure threshold during normal periods and during peak periods.

[0041] Step S302: Calculate the ratio of the system water demand to the average water demand of the system in each time period; perform nonlinear mapping on the ratio to generate the peak sensitivity coefficient for each time period; the peak sensitivity coefficient corresponding to the time period in which the system water demand is greater than the average water demand of the system in the period is greater than 1.

[0042] Furthermore, after completing the time-varying hydraulic simulation in step S301, this embodiment has obtained the total system water demand for each time period (i.e., the sum of water demands from all users within that time period). This step first calculates the ratio between the water demand for each time period and the average water demand for the entire cycle. For example, if the water demand for a certain time period is 1.2 times the average, then the ratio is 1.2. Then, this ratio is subjected to nonlinear mapping processing to generate a peak sensitivity coefficient for each time period. This nonlinear mapping processing is as follows: when the water demand is not greater than the average, the coefficient is 1; when the water demand is greater than the average, the coefficient is 1 plus an adjustment parameter multiplied by the excess proportion of the water demand. Since the adjustment parameter is greater than 0, the excess proportion is amplified, so the peak sensitivity coefficient of the time period with the larger water demand is significantly greater than 1. The core function of this nonlinear mapping is to avoid the weight increase of peak periods being too gradual, but to consciously strengthen the influence of peak periods, so that subsequent index calculations can more sensitively reflect the peak exacerbation phenomenon.

[0043] Step S303: Using the product of the system water demand in each time period and the peak sensitivity coefficient as a comprehensive weight, the system resilience index in each time period is weighted and averaged to obtain the peak sensitivity resilience index.

[0044] Furthermore, after obtaining the peak-time sensitivity coefficient for each time period, this step multiplies the system water demand for each time period by the corresponding peak-time sensitivity coefficient to obtain the comprehensive weight for that time period. The reason for introducing the system water demand is that the total system water demand itself is also a dimension for measuring the importance of a time period: a time period with high water demand means a larger water-consuming population and greater service pressure, and should therefore be given a higher weight. Finally, the system resilience index (i.e., MRI, representing the system's pressure margin for that time period) for each time period is multiplied by its comprehensive weight, then summed over all time periods, and finally divided by the sum of the comprehensive weights to obtain a weighted average. The resulting peak-time sensitivity resilience index (PIMRI) reflects both the additional weight generated by high water demand during peak periods and the peak-time sensitivity coefficient amplified through nonlinear mapping, thus more accurately reflecting the system's vulnerability under peak loads.

[0045] Step S304: Apply hydraulic disturbance to the preset potential node, and select candidate nodes from the potential nodes based on the degree of pressure improvement of the weak node after the disturbance.

[0046] In one optional implementation, step S304 includes: At each of the preset potential nodes, a virtual head increment of a preset amplitude is applied, and the time-varying hydraulic simulation is re-executed to obtain the updated pressure value of each vulnerable node. Calculate the weighted sum of the pressure improvement amount of each weak node before and after the perturbation is applied to each potential node, and use it as the pressure improvement degree of the corresponding potential node; Potential nodes whose pressure improvement is below a preset improvement threshold are removed, and the remaining potential nodes are selected as candidate nodes.

[0047] Further, the candidate node selection process involves first artificially applying a fixed virtual head increment, for example, 20% to 50% of the average service head, to each pre-defined potential node (i.e., the location in the pipeline where a pumping station might be built). Head refers to the height to which a pump can lift water; increasing the head is equivalent to increasing the water pressure at that node. Then, the variable hydraulic simulation is run again, recording the latest pressure values ​​of the originally weak nodes after the perturbation. Next, the pressure improvement degree of each potential node is calculated: first, the pressure deficiency of each weak node before the perturbation (minimum service pressure minus actual pressure, set to 0 if non-positive) and the pressure deficiency after the perturbation are calculated, and the difference is the pressure deficiency improvement amount for that node. Then, using the original pressure deficiency of each weak node as a weight, the improvement amounts of all weak nodes are weighted and summed, and finally divided by the perturbation amplitude (i.e., the virtual head increment) to obtain the comprehensive score of the potential node. The higher the score, the more significant the improvement effect of the node on the low-pressure area. Finally, nodes with scores below a preset threshold are removed, and nodes with higher scores are retained as candidate nodes in the subsequent optimization model.

[0048] Step S305: Construct a multi-objective optimization model; the multi-objective optimization model takes at least the peak-time sensitivity resilience index as the optimization objective, and the discrete variables of the candidate node's location and the continuous variables of its size as decision variables.

[0049] In one optional implementation, the optimization objectives of the multi-objective optimization model also include minimizing the economic cost of construction and operation and maximizing the overall reliability of the system; The constraints of this multi-objective optimization model include the lower limit constraint of node pressure, the pump flow rate constraint, and the pipe section flow velocity constraint.

[0050] Furthermore, the multi-objective optimization model constructed in step S305, in addition to using the peak-time sensitivity resilience index as the optimization objective, also includes two other optimization objectives: minimizing the economic cost of construction and operation and maximizing the overall system reliability. The economic cost of construction and operation includes the construction investment of the pumping station (related to the number and scale of the pumping stations) and the operating electricity cost over the entire life cycle (calculated based on pump energy consumption and electricity prices at each time period). The overall system reliability is usually defined as the average degree to which the pressure of each node meets the demand throughout the entire simulation period, such as the system periodic reliability PRsys, which integrates the pressure service level of all nodes at each time period. In addition, the model's constraints include at least three types: node pressure lower limit constraints (the pressure of any node at any time must not be lower than the minimum service pressure, a core hard constraint to ensure water supply quality), pump flow constraints (pumping stations must operate within the flow range allowed by their performance curves to avoid exceeding operating conditions), and pipe velocity constraints (excessive flow velocity may cause water hammer and pipe damage, while excessively low flow velocity may lead to water quality problems). By combining the above three objectives and three types of constraints, the optimization model can more comprehensively reflect the actual needs of the project and ensure that the pump station layout scheme obtained achieves a reasonable balance between economy, reliability and engineering feasibility.

[0051] Step S306: A multi-objective evolutionary solution strategy is adopted to solve the multi-objective optimization model and obtain a non-dominated solution set. This multi-objective evolutionary solution strategy refers to the process of generating an initial population based on a hybrid encoding of discrete location variables and continuous scale variables, performing crossover and mutation operations in the evolutionary iteration, dynamically updating the feasible solution file and near-feasible solution file that retains extreme value solutions, and generating new solution individuals based on sampling the local statistical distribution of elite solutions.

[0052] In one optional implementation, step S306 includes: The discrete variable for the location of the candidate node is encoded in binary, and the continuous variable of this size is encoded in real number to generate an initial population with mixed encoding. Based on the initial population, an evolutionary iteration is performed. In each generation of the evolutionary iteration process, the step size factor is calculated according to the hierarchical mechanism of the gray wolf optimization algorithm. The position of the continuous variable is directly updated, and the discrete variable is updated collaboratively through the transfer function to generate the offspring population.

[0053] In each generation of the evolutionary iteration process, the feasible solution file and the near-feasible solution file are dynamically updated for dual-file guidance; the feasible solution file stores solutions that satisfy all constraints, and the near-feasible solution file stores solutions with constraint violation degrees less than a dynamic threshold; Based on the feasible solution file, a predetermined number of elite solutions are extracted. The covariance matrix is ​​constructed using the local statistical distribution of the elite solutions. Based on the covariance matrix, local covariance learning is performed to generate new individual solutions that satisfy the constraints of the multi-objective optimization model.

[0054] When updating the feasible solution file and near-feasible solution file, an extreme point retention strategy is implemented to retain the extreme solutions that are concentrated at the boundary positions in each optimization objective direction.

[0055] Furthermore, the solution process of the multi-objective optimization model first encodes the decision variables. Discrete variables for site selection are encoded using binary codes (0 indicates no pump station, 1 indicates construction), while continuous variables for scale are encoded using real numbers (representing the pump curve scaling factor). These two codes are combined to form an individual. After the initial population is randomly generated, in each generation of evolutionary iterations, the step size factor is calculated according to the hierarchical mechanism of the Grey Wolf optimization algorithm. The continuous variables are directly updated in position, and the discrete variables are updated collaboratively using a transfer function to generate offspring populations. Simultaneously, the algorithm dynamically updates the feasible solution file and the near-feasible solution file for dual-file guidance: maintaining two files: a feasible solution file (storing solutions that satisfy all constraints) and a near-feasible solution file (storing solutions with constraint violations less than a dynamic threshold). When updating the files, an extreme point retention strategy is implemented to preserve the extreme solutions where non-dominated solutions are concentrated at the boundary positions along each optimization objective direction. These extreme solutions represent the boundary solutions that achieve the optimal state for a specific optimization objective (such as maximizing peak-time sensitivity resilience or minimizing economic cost). Preserving them prevents the population from losing edge information during evolutionary iterations, avoids the degenerate shrinkage of the Pareto front, and thus ensures that the final solution set has the widest possible distribution, providing realistic extreme preference options for subsequent decisions. Furthermore, the algorithm extracts a certain number of elite solutions from the feasible solution archive, constructs a covariance matrix using the local statistical distribution of these elite solutions in the decision space (e.g., calculating the mean and covariance), and performs local covariance learning and sampling based on this covariance matrix to generate new candidate solutions. This approach utilizes the local structural information of elite solutions, improving search efficiency and solution set quality.

[0056] Step S307: Perform multi-attribute decision sorting on the non-dominated solution set to obtain the pressurization facility layout scheme for the target water supply network.

[0057] In one optional implementation, step S307 includes: The weight vectors of each optimization objective are determined based on preset decision preferences; these decision preferences include cost preference, equilibrium preference, or performance preference. Based on this weight vector, each optimization objective is normalized and weighted, and the distance between each solution and the positive ideal solution and the negative ideal solution is calculated, thereby obtaining the relative fitting progress. Sort the solutions in descending order of their relative matching progress, and output the sorted list of solutions.

[0058] Furthermore, the specific process of multi-attribute decision ranking for the obtained non-dominated solution set in this embodiment is as follows: First, based on actual engineering needs, one of three preset decision preferences is selected: cost preference (emphasizing investment and operational economy), equilibrium preference (equal importance of all three), or performance preference (emphasizing reliability and resilience). Each preference corresponds to a set of weight vectors, and the sum of the weights of the three objectives (cost, reliability, and peak-time sensitivity resilience) is 1. Then, the objective values ​​of each scheme in the non-dominated solution set are normalized (eliminating dimensional differences), and then weighted according to the weights to obtain a weighted normalized matrix. Next, the positive ideal solution (the optimal value after weighting each objective) and the negative ideal solution (the worst value after weighting each objective) are calculated, and the Euclidean distance from each scheme to the positive and negative ideal solutions is calculated. Finally, the relative schedule is used as the evaluation index, that is, the distance to the negative ideal solution divided by the sum of the distances to the positive and negative ideal solutions. The closer this value is to 1, the better the scheme. All schemes are sorted from largest to smallest according to the relative schedule, and the sorted scheme list is output for engineers to select according to actual conditions.

[0059] Please see Figure 4 The diagram illustrates a third type of multi-objective optimization layout method for booster pump stations in a water supply network based on peak-time sensitive resilience. This embodiment can be implemented on a computer system equipped with suitable computing resources, including a processor, memory, storage devices, and necessary input / output devices. The software environment needs to include a core engine for hydraulic modeling and pressure-driven analysis of the water supply network (such as the EPANET 2.2 open-source library or its commercial equivalent), and a programming platform (such as Python or MATLAB) for implementing optimization algorithms and data analysis.

[0060] Before implementation, complete basic data on the target water supply network must be prepared, including at least: Topology and attribute data: ID, elevation, and basic water demand (baseline flow rate) of all nodes; ID, start and end nodes, length, diameter, and roughness coefficient (Hayzen-Williams coefficient or Darcy friction factor) of all pipe segments; water level-flow rate relationship or constant head of the water source (clear water tank, water plant); performance curves (head-flow rate relationship) of existing water pumps and valve status.

[0061] Operating mode data: 24-hour water usage pattern variation curve (pattern multiplier) for at least one typical day (such as the peak day) to simulate the time-varying operating conditions of the system.

[0062] Constraints and performance parameters: Minimum service pressure (minimum free head) required for each node; maximum and minimum permissible speed or operating range of the pump.

[0063] Economic parameters: investment cost coefficient per unit flow (or per unit power) for pump station construction, electricity price (time-of-use), discount rate, design life, efficiency of pump station electromechanical equipment, etc., are used to calculate the total life cycle cost (including the discount of initial investment and the discount of operating electricity costs).

[0064] First, using the above data, a hydraulic model of the water supply network is constructed in a hydraulic simulation engine and set to pressure-driven analysis (PDA) mode to realistically simulate the actual outflow of nodes under low-pressure conditions. An extended time-period simulation of a complete cycle (e.g., 24 hours, with a time step of 1 hour) is run to obtain the data for all nodes at all time periods. t Pressure values ​​( = 1, 2, ..., T) P j ( t ) and actual traffic q j ( t ).

[0065] Please see Figure 5 The diagram illustrates the calculation principle of the Peak-Time Sensitive Integrated Resilience Index (PIMRI). This embodiment constructs a system-level resilience index that more sensitively reflects pressure deterioration during peak periods using the PIMRI. The specific steps are as follows: First, calculate the corrected resilience index of MRI at each time period. t For a single time period t The system's modified resilience index is calculated as the ratio of the actual available remaining energy of all nodes to the theoretically maximum available remaining energy, as shown in the following formula: ; in, for Time period nodes The water demand, For nodes The actual pressure during that period For nodes Minimum required pressure, This represents the total number of demand nodes. This index reflects the... t The relative size of the resilience margin that the system still possesses after meeting its needs, which can be used to resist disturbances.

[0066] The total water demand of the system for each time period is obtained as follows: Q t : ; This value represents the actual water supply under pressure-driven analysis, and is equal to the baseline water demand when there is no pressure deficiency.

[0067] Next, determine the peak-time sensitive adjustment parameters.α , α The adjustment parameter is greater than 0, which controls the degree of weight amplification of peak periods in the overall evaluation. α The higher the value, the stronger the focus on peak hours. For example, it is recommended to take... α = 2.0. Implementers can perform sensitivity analysis (e.g., take...) α = 0.5, 1.0, 1.5, 2.0, 2.5), observe the changes in PIMRI values ​​and their contribution weights at each time period, in order to select those that conform to local water supply security policies. α Value. Typically, α = 2 can achieve a good balance between significantly highlighting the peak impact and maintaining the overall stability of the indicators.

[0068] For MRI t The peak-time sensitive weighted average is calculated using the following formula: ; in, T This represents the total number of time periods. For the first t Total system water demand for a given period of time. For the first t The system's adjusted resilience index over a given period of time. For the first t The peak sensitivity coefficient for a given time period is calculated using the following formula: ; in, and These represent the average water demand and the maximum water demand over the entire simulation period, respectively. α For peak-time sensitive adjustment parameters greater than 0; when > (Average water demand), this coefficient is greater than 1, thus amplifying the MRI results during this period. t The contribution of PIMRI to the final PIMRI value is smaller during off-peak periods; conversely, its contribution decreases during off-peak periods. This makes PIMRI more effective than traditional periodic averaging MRI or simple demand-weighted PIMRI in reflecting the vulnerability of a system under peak load.

[0069] To narrow the optimization search space, this embodiment aims to select the most effective candidate pressurization nodes from among numerous nodes to improve the target low-pressure area.

[0070] Based on the above periodic simulation results, services with pressure lower than their minimum service pressure during at least one period were selected. All nodes j This forms the initial low-pressure node set L.

[0071] Construct a pressure-sensitive matrix and set a standard virtual head increment Δ. HFor example, Δ H It can be taken as 30% of the system's average service head (for example, if the average service head is 30m, then Δ H = 9m). Iterate through each non-water source node in the network sequentially. i (Or, based on engineering experience, limit the scope to potentially buildable areas, such as the end of a pipeline network or near abrupt changes in terrain), and perform the following operations: a) In a network hydraulic model, at the nodes i A virtual head increment Δ is temporarily added at the location. H Boosting facilities (such as virtual water pumps).

[0072] b) Run a pressure-driven simulation (typically targeting the single period of most unfavorable pressure to improve efficiency) to obtain the values ​​of each node in the low-pressure node set L. j New pressure value .

[0073] c) Computation nodes i The boost to the node j The resulting pressure increase value Δ P ij = - .in Let be the original pressure of node j.

[0074] For all candidate nodes i and all low-voltage nodes j Calculations were performed to obtain the pressure increase matrix [Δ]. P ij ].

[0075] For each candidate pressurization node i Calculate its comprehensive score for insufficient pressure recovery in low-pressure areas. R D ( i ): ; ; in, Let L be the number of nodes in the low-pressure node set. To minimize service pressure, For the target node Pressure during the most unfavorable times, Let J be the pressure corresponding to the target node j under the disturbance condition. Node weights; in, This indicates that the pressure on the target node j is insufficient. Represents a node iThe boost can effectively compensate for the target node j Insufficient pressure (to the maximum extent possible) ). R D ( i The value range of ) is [0,1], reflecting the node i The comprehensive ability to recover from insufficient overall pressure. R D ( i ) = 1 means node i The boost pressure can completely compensate for the insufficient pressure at all low-pressure nodes.

[0076] Set a threshold ε (For example ε = 0.001). Filter out all R D ( i )> ε The nodes. For further condensation, it can be categorized by... R D ( i Sort the nodes from largest to smallest, and select the top K nodes (e.g., K = 10) to form the final candidate pressurization node set C. This step ensures that the candidate nodes have direct and effective pressure recovery potential for the low-pressure area.

[0077] This embodiment transforms the engineering problem into a computable mathematical model (i.e., a multi-objective optimization model). For a problem with N candidate nodes (where the cardinality of the set C is |C| = N), a solution (i.e., a layout scheme) is represented using hybrid encoding as follows: ;in, x i ∈{0, 1} is a binary variable, representing the candidate node. i (Its node ID in the original network's node ID corresponding set C is the first) i Whether to build a pumping station (1 for building, 0 for not building) at each node. It is a continuous variable, indicating that if a pumping station is built at this node ( =1), the rated characteristic curve of the selected water pump ( The scaling factor. λ i Essentially, it's in the water pump curve. H 0 and s The scaling factor determines the head-flow performance of the water pump. and The range of available water pump models is determined by this. In the calculation, through... To obtain an effective scaling factor, when x i When = 0, This indicates that there is no pump at this node.

[0078] This embodiment also establishes three conflicting objective functions: 1) Minimize total lifecycle cost : Investment costs ,in Here, is the pump's rated flow rate reference value, and a and b are the fitted cost coefficients. Operating energy cost. By performing a hydraulic simulation over an operating cycle (e.g., 24 hours), the power consumption of all operating pumps during all time periods is calculated, and then discounted to present value based on electricity price and discount rate.

[0079] 2) Maximize system cycle reliability : ,in In the formula For nodes The actual pressure during that period For nodes Minimum required pressure, For nodes The maximum pressure, The total number of nodes required. This represents the total system water demand for that period, calculated in the same way as above. For the system in the first The average state of overall pressure service level during a given time period. This indicator represents the degree to which pressure is met at each node during each time period.

[0080] 3) Maximize peak-time sensitive overall resilience : The calculation method is the same as above.

[0081] The three constraints include: 1) Node pressure constraints: , j , t This is a hard constraint. In optimization algorithms, it is usually converted into constraint violation (CV) for processing. One of the optimization goals is to minimize the CV until it becomes 0.

[0082] 2) Hydraulic balance constraints: These are automatically satisfied by the hydraulic simulation engine each time the objective function is evaluated.

[0083] 3) Variable boundary constraints: .

[0084] Therefore, this multi-objective optimization problem can be formalized as: Minimize F(X) = [ f 1(X), -f 2(X), - f [3(X)], while minimizing the constraint violation degree CV(X). The goal is to find the Pareto optimal solution set that satisfies CV(X)=0.

[0085] Please see Figure 6 The flowchart of the improved multi-objective gray wolf optimization algorithm (CAMOGWO-FN) is shown. This embodiment uses the multi-objective gray wolf optimization algorithm (CAMOGWO-FN) to solve the above multi-objective optimization model. Let the population size be... N p The maximum number of iterations is .

[0086] Perform initialization and randomly generate the initial population. P 0, each individual is randomly initialized. and Run hydraulic simulations to evaluate the performance of each individual component. f 1, f 2, f 3] and constraint violation coefficient (CV). Initialize the feasible file (FA) to empty and the near feasible file (NFA) to empty. Set the near feasible threshold. initial value (like (1% of the median CV in the initial population).

[0087] Please see Figure 7 The diagram shown illustrates the dual-file guidance mechanism of the improved multi-objective gray wolf optimization algorithm (CAMOGWO-FN), in each generation. t The merger of FA and NFA forms the leadership wolf pool. .choose α , β , δ The strategy of the three-headed wolf leader is: a) If the number of individuals in the FA is sufficient (to cover the critical region of the non-dominant front), then select the three individuals with the best distribution from the FA based on their grid crowding distance (or the crowding degree of the target space) as... α , β , δ .

[0088] b) If the number of individuals in the FA is insufficient, all individuals in the FA are selected as part of the leader wolves, and the remaining leader wolves are selected from the NFA according to the CV value from smallest to largest (i.e., the closer to feasibility) and the non-dominant ranking of the target to fill the gap.

[0089] c) If there are no feasible individuals in the FA, then select all from the NFA based on the CV value and the target value.

[0090] This strategy ensures that the search is always guided by high-quality and as feasible a solution as possible.

[0091] Please see Figure 8 The diagram illustrates the local covariance learning mechanism of the improved multi-objective gray wolf optimization algorithm (CAMOGWO-FN) and... Figure 9 The diagram illustrates the hybrid variable update and repair mechanism of the improved multi-objective gray wolf optimization algorithm (CAMOGWO-FN). The solution in FA is adaptively meshed in the normalized objective space. For each non-empty mesh cell B... k Calculate the mean vector of all elite solutions in the decision variable space (the continuous variable part λ). μ k Covariance Matrix When generating offspring, probability is used. (e.g., 0.2) Perform covariance learning sampling: randomly select a grid cell B. k (The selection probability is inversely proportional to the number of solutions within the grid, to facilitate the search for sparse regions), from a multivariate Gaussian distribution N( μ k , A continuous variable vector is generated by sampling in ) λ child This operation is used to learn the local variable association structure of elite solutions and to perform guided local development.

[0092] Continuous variable (λ) update: For each individual, with probability (e.g., 0.6) Perform standard GWO position update (around) α , β , δ wolves); with probability (e.g., 0.2) Perform differential evolution (DE / rand / 1) perturbation; with probability (e.g., 0.2) Perform the above covariance learning sampling. After updating, for Perform boundary repair: If < ,but = ;like > ,but = .

[0093] binary variables ( Update: Statistics on all elite solutions in the current FA and NFA at each level. Frequency of taking 1 For each offspring individual, Independently by probability It is set to 1 if it is not set to 0 otherwise (i.e., Bernoulli sampling). This biases the search towards pump station location combinations that are common in elite solutions.

[0094] Consistency repair: For each pair of decision variables , Forced execution That is, if (If no pumping station is built), then the corresponding Set as its lower limit (or 0) to ensure consistent optimization logic.

[0095] For environmental selection that preserves extreme points, parent and offspring populations are merged for non-dominated ranking. When selecting individuals from the first non-dominated layer F1 to enter the next generation, individuals in F1 are first identified for each target... f 1, f 2, f The optimal values ​​are found on each of the three. f 1 is the smallest. f 2 and f The three extreme points (maximum 3) are directly preserved to the next generation of the population. Then, for the remaining individuals in F1 and subsequent individuals in the non-dominated layers, selection is performed sequentially based on non-dominated level and crowding distance, until... Fill it. This strategy ensures the extensibility of the Pareto front boundary.

[0096] Evaluate the newly generated offspring individuals. Update FA and NFA: Relate FA and NFA to the new population. Individuals with CV=0 are merged, and a non-dominated sort is performed. The FA is then updated to the non-dominated solution set with CV=0 after the merge. The NFA is updated to the non-dominated solution set with CV=0 after the merge. <CV<= The non-dominated solution set. Update the near-feasible threshold. Where c is the attenuation coefficient (e.g., c=5), so that Decrease to 0 with each iteration. Check if it has been reached. If the condition is not met, return to the above steps of dual file guidance and alpha wolf selection; otherwise, output FA as the final Pareto optimal solution set.

[0097] After obtaining the Pareto solution set (containing M non-dominated solutions), the TOPSIS method is used to sort them to aid in the final decision.

[0098] Construct a normalized decision matrix, denoted as _i_. j The first scheme is in the k The value on each target is , k = 1, 2, 3 correspond to respectively f 1 (Cost) f2 (Reliability) f 3 (PIMRI). Due to differences in target dimensions and trends, normalization is required. Regarding cost (lower is better): Regarding reliability and PIMRI (the larger the better): The normalized matrix is ​​obtained. .

[0099] Define a weight vector based on different decision preferences. w = [ w 1, w 2, w 3],Σ w k = 1. Example as follows: Cost-oriented: w = [0.50, 0.25, 0.25] (Focusing on economic efficiency); Equilibrium preference type: w = [0.33, 0.33, 0.34] (the three are balanced); Performance-oriented: w = [0.20, 0.40, 0.40] (Emphasis on reliability and resilience); Calculate the weighted normalized matrix V, where Determine the ideal solution. ,in Negative ideal solution ,in Calculate each solution to and Euclidean distance and Calculate the relative alignment of each solution with the ideal solution. . The larger the value (the closer to 1), the better the overall performance of the solution. (According to...) All options are sorted from largest to smallest value, and the sorted result is the recommended list of options under the current decision preference.

[0100] The following simple examples illustrate the content disclosed in the above embodiments: Example 1: Using the NET3 network provided by EPANET as an example, the effectiveness of this invention in a benchmark test case is verified. The NET3 network includes 97 nodes, 117 pipes, 2 water sources, 3 water tanks, 3 pumping stations, and 2 valves. To simulate a localized low-pressure scenario, the area containing nodes 211-255 was selected, its basic water demand was doubled, and the elevation of these nodes was uniformly increased by 54 feet, thus forming a stable low-pressure zone. The minimum service pressure was set to 35 psi (approximately 24.1 meters). Peak-sensitive adjustment parameters.α Take 2.0.

[0101] For candidate node selection, pressure sensitivity analysis (Δ) was performed on nodes surrounding the low-pressure area. H = 50 feet), calculation R D ( i The results show that nodes 251, 247, 239, and 211... R D ( i If the value is significantly greater than 0, it is selected as a candidate pressurization node (indexed as 120-123 in the optimization model).

[0102] For PIMRI index verification, the traditional MRI, demand-weighted IMRI and the PIMRI of this invention were compared and calculated. α = 2) Contributions at different times throughout the entire operating cycle. For example... Figure 10 The chart showing the comparison of the contributions of PIMRI and traditional indicators (IMRI) to resilience indicators at different time periods demonstrates that PIMRI's contribution is significantly higher than IMRI during periods of high system water demand, such as 1 hour, 9-13 hours, and 22-23 hours. This indicates that PIMRI successfully shifts the evaluation weight towards peak periods, more accurately reflecting the system's vulnerability during peak times.

[0103] The optimization problem was solved using both the NSGA-II algorithm and the CAMOGWO-FN algorithm of this invention, with a population size of 100 and a maximum number of evaluations of 30,000. Each algorithm was run 30 times. Please refer to [link to relevant documentation]. Figure 11 The diagram showing the comparison between the total cost and the frontier of the PRsys objective function algorithm is as follows: Figure 12 The diagram showing the comparison between the total cost and the front of the PIMRI objective function algorithm is illustrated. The Pareto front obtained by the CAMOGWO-FN algorithm is significantly smoother and more uniformly distributed than the front obtained by NSGA-II, especially exhibiting better extensibility at both ends of the solution set (the lowest cost end and the highest performance end). Quantitative evaluation uses hypervolume (HV) and inverse generation distance+ (IGD). ＋ The CAMOGWO-FN algorithm yielded an average HV value of 0.5322 for the solution set, higher than NSGA-II's 0.5266; and an average IGD+ value of 0.0007, significantly lower than NSGA-II's 0.0052. This demonstrates that CAMOGWO-FN outperforms NSGA-II in both convergence and distribution.

[0104] Twenty representative Pareto solutions were selected from a typical run of the CAMOGWO-FN algorithm. TOPSIS was applied for multi-attribute decision-making. Based on the characteristics of the Pareto solution set and the TOPSIS ranking results, the optimal solution under different decision preferences was solution P1 (only one booster pump station was built at node 247). =0.95). This scheme performed optimally after comprehensively considering total lifecycle cost, lifecycle reliability, and peak-time sensitive integrated resilience PIMRI, indicating that node 121 is the most controllable key pressurization location in this low-pressure scenario. After implementing this scheme, PRsys improved from 0.4261 to 0.4477, an increase of 0.0216, or 5.07%; PIMRI improved from 0.8427 to 0.8777, an increase of 4.15%, with a cost of 27.7 million yuan. This demonstrates that, through this invention, decision-makers can select the most suitable pressurization pump station scheme and determine key pressurization nodes based on different investment budgets and performance requirements.

[0105] Example 2: Using a real water supply network in a central urban area of ​​a city as an example, this invention is verified for its applicability in large-scale, complex real-world engineering projects. The network model includes 576 nodes, 803 pipes, 2 water plant sources, and multiple areas with consistently low pressure. The minimum service pressure is set at 16 meters. Peak-sensitive adjustment parameters are used. α Take 2.0.

[0106] For candidate node selection, the pressure sensitivity matrix of the entire pipeline network (Δ) is analyzed. H =20 meters), calculate the comprehensive score for insufficient pressure recovery at all non-water source nodes. R D ( i ). Filter out R D ( i Nine nodes (IDs: 209, 525, 516, 505, 527, 17, 507, 16, 498) with a saturation value greater than 0.006 are selected as the candidate pressurization node set. Their spatial distribution can be found in [link to relevant documentation]. Figure 13 The diagram showing the distribution of candidate pressurization nodes in a central urban area of ​​a certain city is mainly located in the northern and central-eastern pressure-deficient areas of the pipeline network.

[0107] The CAMOGWO-FN algorithm (population size 150, maximum number of evaluations 50,000) was used to obtain the Pareto optimal solution set. Compared with the original system without additional pump stations (PRsys = 0.3852, PIMRI = 1.1591), all optimized schemes showed improvements in reliability and resilience. For example, the lowest-cost scheme P1 (building pump stations at nodes 209, 507, and 16, with a total investment of approximately 61.1 million yuan) improved PRsys to 0.4222 (an improvement of 9.61%) and PIMRI to 1.2389 (an improvement of 6.88%). Analysis of the solution set revealed that nodes 209 and 507 appeared in over 90% of the Pareto schemes, making them key control nodes for improving system performance.

[0108] The Pareto solution set was sorted using TOPSIS. Under cost preference, solution P1 is optimal; under equilibrium preference, solution P2 (building pumps at nodes 209 and 507, costing 69.5 million yuan) is optimal; under performance preference, solution P5 (building pump stations at nodes 209, 507, and 16 with higher scale configuration, costing 86.8 million yuan) is optimal. For a comparison of the objective function values ​​of the solutions under the three preferences, please refer to [link to relevant documentation]. Figure 14 The performance comparison chart of the top three solutions ranked by TOPSIS under different decision preferences clearly shows the trade-offs between cost, reliability, and resilience, providing decision-makers with a clear quantitative basis for selection.

[0109] This embodiment also provides a multi-objective optimization layout system for booster pump stations in a water supply network based on peak-time sensitive resilience. This system is used to implement the above embodiments and preferred embodiments, and details already described will not be repeated. As used below, the term "module" can refer to a combination of software and / or hardware that performs a predetermined function. Although the systems described in the following embodiments are preferably implemented in software, hardware implementations, or a combination of software and hardware, are also possible and contemplated.

[0110] This embodiment provides a multi-objective optimization layout system for booster pump stations in a water supply network based on peak-time sensitive resilience, such as... Figure 15 As shown, it includes: The data acquisition and simulation module 1501 is used to construct a hydraulic model based on the basic parameters of the target water supply network and perform time-varying hydraulic simulation to identify weak nodes in the network where the pressure is lower than a preset pressure threshold during normal periods and during peak periods.

[0111] The resilience assessment module 1502 is used to extract the system resilience index for each time period in the time-varying hydraulic simulation results, and to perform weighted calculation on the system resilience index based on the deviation between the system water demand for each time period and the average water demand of the periodic system to obtain the peak-time sensitive resilience index. The candidate node screening module 1503 is used to apply hydraulic disturbance to a preset potential node and screen candidate nodes from the potential nodes based on the degree of pressure improvement of the weak node after the disturbance. The optimization solution engine module 1504 is used to construct a multi-objective optimization model and solve the multi-objective optimization model using a multi-objective evolutionary solution strategy to obtain a non-dominated solution set. The multi-objective optimization model takes at least the peak-time sensitivity and resilience index as the optimization objective and the discrete location variable and continuous scale variable of the candidate node as decision variables. The decision support module 1505 is used to perform multi-attribute decision ranking on the non-dominated solution set to obtain the pressurization facility layout scheme of the target water supply network.

[0112] In some alternative implementations, the toughness assessment module 1502 is also used for: Calculate the ratio of the system's water demand in each time period to the system's average water demand over the period; A nonlinear mapping is performed on this ratio to generate peak sensitivity coefficients for each time period; the peak sensitivity coefficient for the time period when the system's water demand is greater than the system's average water demand for that period is greater than 1. The system resilience index for each time period is obtained by taking the product of the system water demand for each time period and the peak sensitivity coefficient as the comprehensive weight and averaging the system resilience index for each time period.

[0113] In some alternative implementations, the candidate node filtering module 1503 is further configured to: At each of the preset potential nodes, a virtual head increment of a preset amplitude is applied, and the time-varying hydraulic simulation is re-executed to obtain the updated pressure value of each vulnerable node. Calculate the weighted sum of the pressure improvement amount of each weak node before and after the perturbation is applied to each potential node, and use it as the pressure improvement degree of the corresponding potential node; Potential nodes whose pressure improvement is below a preset improvement threshold are removed, and the remaining potential nodes are selected as candidate nodes.

[0114] In some optional implementations, the optimization objectives of this multi-objective optimization model also include minimizing the economic cost of construction and operation and maximizing the overall reliability of the system; The constraints of this multi-objective optimization model include the lower limit constraint of node pressure, the pump flow rate constraint, and the pipe section flow velocity constraint.

[0115] In some alternative implementations, the optimization solver module 1504 is also used for: The discrete variable for the location of the candidate node is encoded in binary, and the continuous variable of this size is encoded in real number to generate an initial population with mixed encoding. Based on the initial population, an evolutionary iteration is performed. In each generation of the evolutionary iteration process, the step size factor is calculated according to the hierarchical mechanism of the gray wolf optimization algorithm. The position of the continuous variable is directly updated, and the discrete variable is updated collaboratively through the transfer function to generate the offspring population.

[0116] In some alternative implementations, during each generation of the evolutionary iteration process, the feasible solution file and the near-feasible solution file are dynamically updated for dual-file guidance; the feasible solution file stores solutions that satisfy all constraints, and the near-feasible solution file stores solutions with constraint violations less than a dynamic threshold. Based on the feasible solution file, a predetermined number of elite solutions are extracted, and the covariance matrix is ​​constructed using the local statistical distribution of the elite solutions. Based on the covariance matrix, local covariance learning is performed to generate new individual solutions that satisfy the constraints of the multi-objective optimization model.

[0117] In some alternative implementations, when updating the feasible solution file and the near-feasible solution file, an extreme point retention strategy is performed to retain the extreme solutions that are concentrated at the boundary positions in each optimization objective direction.

[0118] In some alternative implementations, the decision support module 1505 is further configured to: The weight vectors of each optimization objective are determined based on preset decision preferences; these decision preferences include cost preference, equilibrium preference, or performance preference. Based on this weight vector, each optimization objective is normalized and weighted, and the distance between each solution and the positive ideal solution and the negative ideal solution is calculated, thereby obtaining the relative fitting progress. Sort the solutions in descending order of their relative matching progress, and output the sorted list of solutions.

[0119] Figure 16 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention.

[0120] The following is a detailed reference. Figure 16 The diagram illustrates a structural schematic suitable for implementing an electronic device according to embodiments of the present invention. The electronic device may include a processor (e.g., a central processing unit, graphics processor, etc.) 1601, which can perform various appropriate actions and processes according to a program stored in read-only memory (ROM) 1602 or a program loaded from memory 1608 into random access memory (RAM) 1603. The RAM 1603 also stores various programs and data required for the operation of the electronic device. The processor 1601, ROM 1602, and RAM 1603 are interconnected via a bus 1604. An input / output (I / O) interface 1605 is also connected to the bus 1604.

[0121] Typically, the following devices can be connected to the I / O interface 1605: input devices 1606 including, for example, a touchscreen, touchpad, keyboard, mouse, camera, microphone, accelerometer, gyroscope, etc.; output devices 1607 including, for example, a liquid crystal display (LCD), speaker, vibrator, etc.; memory devices 1608 including, for example, magnetic tape, hard disk, etc.; and communication devices 1609. Communication device 1609 allows electronic devices to communicate wirelessly or wiredly with other devices to exchange data. Although Figure 16 Electronic devices with various devices are shown, but it should be understood that it is not required to implement or have all of the devices shown, and more or fewer devices may be implemented or have instead.

[0122] In particular, according to embodiments of the present invention, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments of the present invention include a computer program product comprising a computer program carried on a non-transitory computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via a communication device 1609, or installed from a memory 1608, or installed from a ROM 1602. When the computer program is executed by the processor 1601, it performs the functions defined in the multi-objective optimization layout method for booster pump stations in a water supply network based on peak-time sensitive resilience according to embodiments of the present invention.

[0123] Figure 16 The electronic device shown is merely an example and should not be construed as limiting the functionality and scope of use of the embodiments of the present invention.

[0124] This invention also provides a computer-readable storage medium. The methods described above according to embodiments of the invention can be implemented in hardware or firmware, or implemented as computer code that can be recorded on a storage medium, or implemented as computer code downloaded via a network and originally stored on a remote storage medium or a non-transitory machine-readable storage medium and then stored on a local storage medium. Thus, the methods described herein can be processed by software stored on a storage medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware. The storage medium can be a magnetic disk, optical disk, read-only memory, random access memory, flash memory, hard disk, or solid-state drive, etc.; further, the storage medium can also include combinations of the above types of memory. It is understood that computers, processors, microprocessor controllers, or programmable hardware include storage components capable of storing or receiving software or computer code. When the software or computer code is accessed and executed by the computer, processor, or hardware, it implements the multi-objective optimization layout method for booster pump stations in a water supply network based on peak-time sensitive resilience shown in the above embodiments.

[0125] A portion of this invention can be applied as a computer program product, such as computer program instructions, which, when executed by a computer, can invoke or provide the methods and / or technical solutions according to the invention through the operation of the computer. Those skilled in the art will understand that the forms in which computer program instructions exist in a computer-readable medium include, but are not limited to, source files, executable files, installation package files, etc. Correspondingly, the ways in which computer program instructions are executed by a computer include, but are not limited to: the computer directly executing the instructions, or the computer compiling the instructions and then executing the corresponding compiled program, or the computer reading and executing the instructions, or the computer reading and installing the instructions and then executing the corresponding installed program. Here, the computer-readable medium can be any available computer-readable storage medium or communication medium accessible to a computer.

[0126] Although embodiments of the invention have been described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of the invention, and all such modifications and variations fall within the scope defined by the invention.

Claims

1. A multi-objective optimization layout method for booster pump stations in a water supply network based on peak-time sensitive resilience, characterized in that, The method includes: A hydraulic model is constructed based on the basic parameters of the target water supply network, and a time-varying hydraulic simulation is performed to identify weak nodes in the network where the pressure is lower than a preset pressure threshold during normal periods and during peak periods. Extract the system resilience index for each time period from the time-varying hydraulic simulation results, and calculate the system resilience index by weighting it according to the deviation between the system water demand for each time period and the average water demand of the periodic system, to obtain the peak-time sensitive resilience index. Hydraulic disturbances are applied to preset potential nodes, and candidate nodes are selected from the potential nodes based on the degree of pressure improvement of the weak nodes after the disturbance. Construct a multi-objective optimization model; the multi-objective optimization model takes at least the peak time sensitivity resilience index as the optimization objective, and the discrete variables of the candidate node's location and the continuous variables of its size as decision variables; A multi-objective evolutionary solution strategy is used to solve the multi-objective optimization model to obtain a non-dominated solution set; The non-dominated solution set is sorted by multi-attribute decision to obtain the pressurization facility layout scheme of the target water supply network.

2. The method according to claim 1, characterized in that, The system resilience index is calculated by weighting the deviations between the system water demand in each time period and the average water demand of the system over a period of time, resulting in a peak-time sensitive resilience index, including: Calculate the ratio of the system's water demand in each time period to the system's average water demand over the period; The ratio is nonlinearly mapped to generate peak sensitivity coefficients for each time period; the peak sensitivity coefficient for the time period when the system water demand is greater than the average water demand of the periodic system is greater than 1. The system resilience index for each time period is obtained by taking the product of the system water demand for each time period and the peak sensitivity coefficient as a comprehensive weight and averaging the index for each time period.

3. The method according to claim 1, characterized in that, The process of applying hydraulic disturbance to preset potential nodes, and selecting candidate nodes from the potential nodes based on the degree of pressure improvement of the weak nodes after the disturbance, includes: At each of the preset potential nodes, a virtual head increment of a preset amplitude is applied, and the time-varying hydraulic simulation is re-executed to obtain the updated pressure value of each of the weak nodes. Calculate the weighted sum of the pressure improvement amount of each weak node before and after the perturbation is applied to each potential node, and use it as the pressure improvement degree of the corresponding potential node; Potential nodes whose pressure improvement is below a preset improvement threshold are removed, and the remaining potential nodes are selected as candidate nodes.

4. The method according to claim 1, characterized in that, The optimization objectives of the multi-objective optimization model also include minimizing the economic costs of construction and operation and maximizing the overall reliability of the system; The constraints of the multi-objective optimization model include the lower limit constraint of node pressure, the pump flow rate constraint, and the pipe section flow velocity constraint.

5. The method according to claim 1, characterized in that, The method of solving the multi-objective optimization model using a multi-objective evolutionary solution strategy includes: The discrete variables for the location of the candidate nodes are encoded using binary encoding, and the continuous variables for scale are encoded using real numbers to generate an initial population with mixed encoding. Based on the initial population, an evolutionary iteration is performed. In each generation of the evolutionary iteration process, the step size factor is calculated according to the hierarchical mechanism of the gray wolf optimization algorithm. The position of the continuous variables is directly updated, and the discrete variables are updated collaboratively through the transfer function to generate the offspring population.

6. The method according to claim 5, characterized in that, In each generation of the evolutionary iteration process, the feasible solution file and the near-feasible solution file are dynamically updated for dual-file guidance; the feasible solution file stores solutions that satisfy all constraints, and the near-feasible solution file stores solutions with constraint violation degrees less than a dynamic threshold; Based on the feasible solution file, a preset number of elite solutions are extracted, and a covariance matrix is ​​constructed using the local statistical distribution of the elite solutions; Based on the covariance matrix, local covariance learning is performed to generate new individual solutions that satisfy the constraints of the multi-objective optimization model.

7. The method according to claim 6, characterized in that, When updating the feasible solution file and near-feasible solution file, an extreme point retention strategy is implemented to retain the extreme solutions that are concentrated at the boundary positions in each optimization objective direction.

8. The method according to any one of claims 1 to 7, characterized in that, The multi-attribute decision ranking of the non-dominated solution set includes: The weight vectors of each optimization objective are determined based on preset decision preferences; the decision preferences include cost preference, equilibrium preference, or performance preference. Based on the weight vector, each optimization objective is normalized and weighted, and the distance between each solution and the positive ideal solution and the negative ideal solution is calculated to obtain the relative fitting progress. Sort the solutions in descending order of relative application progress and output the sorted list.

9. A multi-objective optimization layout system for booster pump stations in a water supply network based on peak-time sensitive resilience, characterized in that, The system includes: The data acquisition and simulation module is used to construct a hydraulic model based on the basic parameters of the target water supply network and perform time-varying hydraulic simulation to identify weak nodes in the network where the pressure is lower than a preset pressure threshold during normal periods and during peak periods. The resilience assessment module is used to extract the system resilience index for each time period in the time-varying hydraulic simulation results, and to perform weighted calculation on the system resilience index based on the deviation between the system water demand for each time period and the average water demand of the periodic system to obtain the peak-time sensitive resilience index. The candidate node screening module is used to apply hydraulic disturbance to a preset potential node and screen candidate nodes from the potential nodes based on the degree of pressure improvement of the weak node after the disturbance. An optimization solution engine module is used to construct a multi-objective optimization model and to solve the multi-objective optimization model using a multi-objective evolutionary solution strategy to obtain a non-dominated solution set; the multi-objective optimization model takes at least the peak-time sensitivity resilience index as the optimization objective and the discrete location variables and continuous scale variables of the candidate nodes as decision variables; The decision support module is used to perform multi-attribute decision ranking on the non-dominated solution set to obtain the pressurization facility layout scheme of the target water supply network.

10. An electronic device, characterized in that, include: The system includes a memory and a processor, which are interconnected. The memory stores computer instructions, and the processor executes the computer instructions to perform a multi-objective optimization layout method for booster pump stations in a water supply network based on peak-time sensitive resilience, as described in any one of claims 1 to 8.

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