A method for optimizing selection of water supply pipeline seismic retrofitting scheme based on pipe network energy index

Abstract

This paper presents an optimization method for seismic retrofitting of water supply pipelines based on pipeline energy indices, belonging to the field of seismic safety assessment and optimization of water supply networks. The method sets the pipeline retrofitting mode according to pipeline parameters, serving as the variable in the seismic retrofitting optimization model. A pipeline energy index reflecting the impact of seismic damage to pipelines is proposed and used as the objective function of the seismic retrofitting optimization model. A multi-objective optimization model is established, with pipeline retrofitting measures as optimization variables and maximizing the pipeline energy index and minimizing pipeline retrofitting costs as optimization objectives. The multi-objective optimization model for seismic retrofitting of water supply pipelines is solved, and a retrofitting scheme is selected. The seismic optimization scheme using the pipeline energy index achieves similar results to the scheme using a large number of hydraulic models to calculate the post-earthquake water supply satisfaction rate index, while reducing the pipeline optimization calculation time and improving computational efficiency.

Description

Technical Field

[0001] This invention relates to an optimization method for seismic retrofitting schemes of water supply pipelines based on pipeline energy indicators, belonging to the field of seismic safety assessment and optimization of water supply pipelines. Background Technology

[0002] Water supply networks are a crucial component of urban lifeline engineering and a vital infrastructure for maintaining basic urban functions. Under the influence of strong earthquakes, numerous water supply pipelines are damaged, leading to a decrease in water supply capacity and consequently impacting post-disaster urban recovery and reconstruction. Pre-earthquake modifications and optimizations of pipelines can improve the seismic resilience of water supply networks, thereby enhancing the safety and reliability of urban water supply.

[0003] Currently, in the research and application of seismic retrofitting schemes for water supply pipelines, the optimization model generally uses the following approach: the post-earthquake hydraulic function satisfaction rate of the water supply network is the objective function, the retrofitting cost is the constraint, and the pipeline retrofitting measures (such as replacing pipe materials or increasing pipe diameter) and the network topology are the optimization variables. Since the uncertainty of earthquake damage is represented by the pipeline failure probability, the Monte Carlo stochastic simulation method is generally used to calculate the objective function (hydraulic function index) for each candidate scheme during the optimization model solution process. This requires a large amount of hydraulic calculation of the pipeline network, resulting in long computation time and low computational efficiency. Therefore, it is necessary to propose other indices to replace the hydraulic function index as the objective function for the seismic retrofitting optimization of water supply pipelines, while simultaneously requiring that the pipeline network corresponding to the optimized retrofitting scheme obtained based on this alternative index still has a high post-earthquake hydraulic function satisfaction rate. Summary of the Invention

[0004] This invention first proposes a pipeline network energy index to reflect the impact of seismic damage on pipelines, and uses this index as the objective function of an optimization model for seismic retrofitting of pipelines to solve for seismic retrofitting measures. The proposed pipeline network energy index reflects the probability of seismic failure of pipelines and the impact of seismic-induced pipeline damage and leakage points on the overall energy of the pipeline network. Pipeline retrofitting measures reduce the probability of seismic failure, thereby improving the value of the pipeline network energy index. The proposed pipeline network energy index is a holistic index, eliminating the need for hydraulic function calculations for each pipeline retrofitting optimization option, thus exhibiting high computational efficiency.

[0005] Step 1: Set the pipeline modification method according to the pipeline network parameters.

[0006] Before carrying out seismic retrofitting and optimization of water supply pipelines, it is necessary to determine the available retrofitting methods based on pipeline attribute parameters (pipe material, pipe diameter, interface type, etc.), site conditions, and seismic intensity, such as replacing pipe material or increasing pipe diameter.

[0007] Step 2: Determine the quantitative indicators of the objective function for pipeline optimization and renovation.

[0008] When optimizing seismic retrofitting of water supply pipelines, the post-earthquake water supply satisfaction rate (SSIQ) index, calculated based on a hydraulic model, can be used as the optimization objective of the optimization model. The expression for the post-earthquake water supply satisfaction rate (SSIQ) is as follows:

[0009]

[0010] In the formula, N n q represents the number of user nodes in the pipeline network. i Let q be the water distribution volume of the i-th user node under post-earthquake damage conditions; i * Let L be the actual water demand (distribution) of the i-th user node under normal fault-free water supply conditions (L / s).

[0011] This invention uses an index R based on pipeline energy to replace the post-earthquake water supply satisfaction rate index SSIQ of the pipeline network, and takes the pipeline energy index R as the optimization objective of the pipeline seismic retrofit optimization model. The calculation expression of the index R is as follows:

[0012]

[0013] In the formula, R is the energy value of the pipeline network, and NN i P is the number of pipes connected to node i; j N represents the failure probability of pipe j connected to node i under seismic load; n q represents the total number of user nodes in the water supply network. i * It is the water distribution volume (m³) of user node i under normal operating conditions. 3 / s); h i It is the total head (m) of user node i under normal operating conditions; h i * N is the minimum head (m) of user node i; m P represents the total number of pipes in the network. fm Q represents the failure probability of pipe m under seismic load; m The flow rate (m³) of pipeline m under normal operating conditions 3 / s); h m1 and h m2 These represent the total head (m) at the starting and ending points of pipeline m under normal operating conditions; QR r The outflow rate (m³) of water source r under normal operating conditions 3 / s); H r The total head (m) of the water source r under normal operating conditions; N r This represents the total number of water sources in the pipeline network.

[0014] Among them, seismic retrofitting measures for pipelines can reduce the probability of pipeline failure P under seismic loading. j and P fm As can be seen from equation (2), when calculating the R index corresponding to different renovation schemes, it is only necessary to calculate the pipeline failure probability corresponding to the scheme, and it is not necessary to calculate the post-earthquake hydraulic function state of the pipeline network corresponding to the renovation scheme. The pipeline failure probability is calculated using an empirical statistical method based on historical earthquake damage data.

[0015] The physical meaning of the pipeline network energy index R. Since the total head (m) at a node represents the mechanical energy per unit weight of fluid, the product of the total head and the flow rate represents the total mechanical energy of the flow. In the numerator, E1 represents the energy actually reaching the user node under seismic load, reflecting the impact of the probability of adjacent pipeline failure due to seismic damage on the node's energy supply. The numerator E2 represents the energy consumption of the pipeline network due to pipeline leakage caused by seismic damage. The denominator E3 represents the maximum energy redundancy value under normal operating conditions of the pipeline network. This represents the total energy input from the water source into the pipe network. This represents the minimum energy required for a user node.

[0016] Step 3: Establish a multi-objective optimization model for seismic retrofitting of water supply pipelines.

[0017] (1) Objective function setting: Taking pipeline renovation measures as optimization variables, and maximizing pipeline energy index and minimizing pipeline renovation cost as optimization objectives, a multi-objective optimization model is established as follows:

[0018] max R(X)(3)

[0019] min CC(4)

[0020] In the formula: X = {} is the set of different renovation schemes for the water supply network (the renovation method is provided in the first step); R(X) is the index value corresponding to the scheme; CC is the investment cost of seismic retrofitting of the pipeline.

[0021] (2) Calculation of renovation price: The formula for calculating the renovation price CC of the entire pipeline network is as follows:

[0022]

[0023] In the formula, N m K represents the total number of pipes in the network. m To indicate measures taken to modify pipeline m, such as K. m ={0,1} represents {no modification, modification} respectively; D m For the m-th pipe, use K m The unit length modification cost (yuan / m) corresponding to the modification measures; L mLet m be the length (m) of the m-th pipe.

[0024] Step 4: Solve the multi-objective optimization model for seismic retrofitting of water supply pipelines and select a retrofitting scheme.

[0025] The optimization model shown in equations (3) to (5) is solved using an intelligent evolutionary algorithm, and the Pareto front distribution map of the optimized renovation scheme is obtained. Based on the annual renovation budget, multiple schemes near the Pareto front point corresponding to the renovation price are selected to form a set of alternative renovation schemes. The post-earthquake water supply satisfaction rate (SSIQ) of the selected alternative scheme set is calculated according to equation (1), and the scheme with the maximum SSIQ value is selected as the final renovation scheme.

[0026] The aforementioned method for optimizing water supply pipeline seismic retrofitting schemes based on pipeline energy indices utilizes the pipeline energy index R as the objective function for pipeline performance during the solution process of the seismic retrofitting optimization model. This R represents the post-earthquake state of the pipeline corresponding to the retrofitting scheme, eliminating the need to calculate the post-earthquake hydraulic model of the pipeline for this retrofitting scheme. This reduces the computation time for pipeline optimization and improves computational efficiency. The results of using the pipeline energy index for seismic retrofitting schemes are comparable to those of schemes using numerous hydraulic models to calculate the post-earthquake water supply satisfaction rate. Attached Figure Description

[0027] Appendix Figure 1 This is a flowchart of the present invention, "An Optimization and Selection Method for Seismic Retrofitting Schemes of Water Supply Pipelines Based on Network Energy Indicators";

[0028] Appendix Figure 2 Pipeline flow and node water consumption distribution diagrams for the implementation case;

[0029] Appendix Figure 3 The pipeline diameter and node elevation distribution map for the implementation case;

[0030] Appendix Figure 4 A comparison chart showing the effects of the optimization schemes obtained by this method in the implementation case;

[0031] Appendix Figure 5 This is a comparison chart showing the running time of the optimized model in the implementation case. Detailed Implementation

[0032] To better understand and implement this invention, the following detailed description is provided in conjunction with specific embodiments.

[0033] Step 1: Set the pipeline modification method according to the pipeline network parameters.

[0034] The example is a Modena pipe network, attached. Figure 2 and attached Figure 3These figures represent the distribution of flow rate, water consumption at nodes, pipeline diameter, and node elevation in the Modena pipeline network. Pipelines with diameters < DN200mm are gray cast iron pipes, while those with diameters between DN200 and 700mm are ductile iron pipes. The seismic load intensity is based on the "China Seismic Intensity Scale," with seismic intensity IX (PGV = 55.5 cm / s) for damage scenario 1 and intensity X (PGV = 119 cm / s) for damage scenario 2.

[0035] Five optional modification measures are available for each pipeline, including: increasing the pipe diameter by 50mm, increasing the pipe diameter by 100mm, replacing the pipe material, replacing the pipe material and increasing the pipe diameter by 50mm, and replacing the pipe material and increasing the pipe diameter by 100mm. The unit length cost for pipeline modification is based on the pipeline investment cost in the "Water Supply and Drainage Manual".

[0036] Step 2: Determine the quantitative indicators of the objective function for pipeline optimization and renovation.

[0037] The pipeline energy index R is used as the optimization objective function and as a substitute index for the post-earthquake water supply satisfaction rate (SSIQ) of the water supply network.

[0038] Step 3: Establish a multi-objective optimization model for seismic retrofitting of water supply pipelines.

[0039] Based on equations (3) to (5) as multi-objective functions, and pipeline renovation measures as optimization variables, a multi-objective optimization model for seismic retrofitting of water supply pipelines is established.

[0040] Step 4: Solve the multi-objective optimization model for seismic retrofitting of water supply pipelines and select a retrofitting scheme.

[0041] The NSGA-II method was used to solve the multi-objective optimization model, and the Pareto front of the optimized scheme was obtained. The solution time of the optimization model was recorded. Among the Pareto fronts obtained by the optimization model, three alternative schemes were selected for the total renovation budgets {8 million, 12 million, and 16 million}, and the SSIQ value of the alternative scheme set was calculated according to Equation (1). For each budget amount, the scheme with the largest SSIQ was selected as the final optimized renovation scheme. The results are shown in the appendix. Figure 4 As shown; Figure 4 The paper also shows the optimization results obtained when the SSIQ calculated directly using the pipeline hydraulic model is used as the objective function of the optimization model. Figure 4 This indicates that the improvement scheme optimized using the pipeline energy index R as the objective function yields results similar to the original scheme optimized using SSIQ as the objective function. (Appendix) Figure 5 The figures represent the running time of the two optimization models when R and SSIQ are used as the objective functions, respectively. It can be seen that the model using R as the objective function has a very short running time. In summary, R can be used as the objective function for the seismic retrofit optimization model of water supply pipelines, exhibiting high computational efficiency.

Claims

1. A method for optimizing the selection of seismic retrofit schemes for water supply pipelines based on pipeline network energy indicators, characterized in that, The method includes the following steps: Step 1: Set the pipeline modification method according to the pipeline network parameters; Before carrying out seismic retrofitting and optimization of water supply pipelines, it is necessary to determine the available retrofitting methods for water supply pipelines based on pipeline attribute parameters, site conditions, and seismic intensity. The pipeline attribute parameters include: pipe material, pipe diameter, and interface type; the available modification methods include: replacing the pipe material and increasing the pipe diameter. Step 2: Determine the quantitative indicators of the objective function for pipeline optimization and renovation; When optimizing the seismic retrofit of water supply pipelines, the post-earthquake water supply satisfaction rate (SSIQ) index, calculated based on a hydraulic model, is used as the optimization objective of the optimization model. The expression for the post-earthquake water supply satisfaction rate (SSIQ) is as follows: ； In the formula, N n q represents the number of user nodes in the pipeline network. i Let q be the water distribution volume of the i-th user node under post-earthquake damage conditions; i * The actual water distribution volume of the i-th user node under normal fault-free water supply conditions is expressed in L / s. The pipeline energy-based index R is used to replace the post-earthquake water supply satisfaction rate index SSIQ. The pipeline energy index R is used as the optimization objective of the pipeline seismic retrofit optimization model. The calculation expression of the index R is as follows: ； In the formula, R is the energy value of the pipeline network, and NN i P is the number of pipes connected to node i; j N represents the failure probability of pipe j connected to node i under seismic load; n q represents the total number of user nodes in the water supply network. i * This is the water distribution volume of user node i under normal operating conditions, in meters. 3 / s;h i This is the total head of user node i under normal operating conditions, in meters (m); h i * N is the minimum head of user node i, in meters; m P represents the total number of pipes in the network. fm Q represents the failure probability of pipe m under seismic load; m The flow rate of the pipeline under normal operating conditions is expressed in m³. 3 / s;h m1 and h m2 QR represents the total head at the starting and ending points of pipeline m under normal operating conditions, in meters; r The outflow rate of water source r under normal operating conditions is expressed in cubic meters (m³). 3 / s;H r The total head of the water source r under normal operating conditions, expressed in meters (m); N r This represents the total number of water sources in the pipeline network; Among them, seismic retrofitting measures for pipelines reduce the probability of pipeline failure P under seismic loading. j and P fm As can be seen from equation (2), when calculating the R index corresponding to different renovation schemes, it is only necessary to calculate the pipeline failure probability corresponding to the scheme, and it is not necessary to calculate the post-earthquake hydraulic function status of the pipeline network corresponding to the renovation scheme; the pipeline failure probability is calculated using an empirical statistical method based on historical earthquake damage data. The physical meaning of the pipeline energy index R: Since the total head at a node represents the mechanical energy per unit weight of fluid, the product of the total head at a node and the flow rate represents the total mechanical energy of the water flow; In the numerator, E1 represents the energy actually reaching the user node under seismic load, reflecting the impact of the probability of adjacent pipeline failure due to seismic damage on the node's energy supply; the numerator E2 represents the energy consumption of the pipeline network due to pipeline leakage caused by seismic damage; the denominator E3 represents the maximum energy redundancy value of the pipeline network under normal operating conditions. This represents the total energy input from the water source into the pipe network. This represents the minimum energy required by a user node; Step 3: Establish a multi-objective optimization model for seismic retrofitting of water supply pipelines; (1) Objective function setting: Taking pipeline renovation measures as optimization variables, and maximizing pipeline energy index and minimizing pipeline renovation cost as optimization objectives, a multi-objective optimization model is established as follows: ； ； In the formula: X = {} represents the set of renovation schemes for the water supply network, and the renovation method is provided in the first step; R(X) is the index value corresponding to the scheme; CC is the investment cost of seismic retrofitting of the pipeline; (2) Calculation of renovation costs: The formula for calculating the renovation cost CC of the entire pipeline network is as follows: ； In the formula, N m K represents the total number of pipes in the network. m K is used to indicate the modifications taken for pipeline m. m ={0,1} represents {no modification, modification} respectively; D m For the m-th pipe, use K m The unit length cost of the renovation measures is expressed in yuan / m; L m This represents the length of the m-th pipe, in meters. Step 4: Solve the multi-objective optimization model for seismic retrofitting of water supply pipelines and select a retrofitting scheme; The optimization model shown in equations (3) to (5) is solved by using an intelligent evolutionary algorithm to obtain the Pareto front distribution map of the optimized renovation scheme; multiple schemes near the Pareto front point corresponding to the renovation price are selected according to the annual renovation budget to form a set of alternative renovation schemes; the post-earthquake water supply satisfaction rate (SSIQ) of the selected alternative scheme set is calculated according to equation (1), and the scheme with the maximum SSIQ value is selected as the final renovation scheme.

2. The method for optimizing and selecting seismic retrofitting schemes for water supply pipelines based on pipeline network energy indicators according to claim 1, characterized in that, In solving the seismic retrofit optimization model for water supply pipelines, the pipeline energy index R is used as the objective function for pipeline performance, representing the post-earthquake state of the pipeline corresponding to the retrofit scheme. This eliminates the need to calculate the post-earthquake hydraulic model of the pipeline corresponding to the retrofit scheme, thus reducing the calculation time for pipeline optimization and improving computational efficiency. The seismic retrofit optimization scheme using the pipeline energy index achieves results similar to the scheme using the post-earthquake water supply satisfaction rate index calculated from numerous hydraulic models.

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