A multi-stage resilience assessment method for sewer networks based on an integrated performance indicator

Abstract

This invention provides a multi-stage resilience assessment method for drainage pipe networks based on comprehensive performance indicators. First, a simulation model of the drainage pipe network in the study area is constructed, and a rainfall scenario is set. Node failure events are identified based on node water level and flow thresholds. Then, a cascade failure simulation model is formed by combining simulation and semi-Markov models. Next, comprehensive performance indicators for the drainage pipe network are constructed, and the discrete states of the drainage pipe network are classified. Based on this, the three-stage resilience and comprehensive resilience of the drainage pipe network are evaluated. This invention, combining a hydrodynamic simulation model with a multi-stage resilience assessment method, can be used to quantitatively measure the propagation of internal node failures and the dynamic evolution of the system's comprehensive performance. It also provides a way to classify the discrete states and critical moments of resilience of the drainage pipe network system under disturbances such as continuous rainfall or hydraulic overload, realizing a quantitative assessment of the multi-stage capacity and comprehensive resilience of the drainage pipe network.

Description

Technical Field

[0001] This invention relates to an urban infrastructure assessment method, specifically a comprehensive resilience assessment method for drainage pipe networks based on comprehensive performance indicators. This method is mainly used to identify the performance evolution patterns of drainage pipe networks under continuous rainfall or hydraulic overload scenarios and to quantitatively assess the resistance, absorption, and recovery capabilities of drainage pipe networks. Background Technology

[0002] In the process of urbanization, drainage pipe networks, as core infrastructure, are crucial for their resilience in the face of extreme weather and sudden failures. Existing technologies often rely on cascading failure models based on topological structures or simplified virtual networks, neglecting the actual physical flow properties of the drainage system, such as the dynamic changes in water level and flow rate. Especially under continuous rainfall, the hydraulic processes within drainage pipe networks become highly complex, making it difficult for traditional robustness calculations to accurately characterize the dynamic characteristics of the entire process from damage to recovery. Summary of the Invention

[0003] To overcome the above problems, this invention provides a method for assessing the resilience of urban drainage pipe networks based on comprehensive performance indicators and a semi-Markov cascade failure model. By dynamically calculating the water level, flow rate, and network connectivity status of pipe network nodes, it achieves a quantitative assessment of node failure propagation and overall system resilience. The specific steps are as follows:

[0004] Step 1: Construct a simulation model of the drainage pipe network in the study area and set up rainfall scenarios;

[0005] Step 2: Identify node failure events based on node water level and flow thresholds;

[0006] Step 3: Combine simulation and semi-Markov simulation to form a cascaded simulation model;

[0007] Step 4: Construct comprehensive performance indicators for the drainage network and classify the discrete states of the drainage network based on its comprehensive performance.

[0008] Step 5: Use the comprehensive performance index built in Step 4 to evaluate the three-stage toughness and overall toughness of the drainage network;

[0009] Step 1 involves constructing a simulation model based on infrastructure parameters such as the node locations, pipe diameters, and slopes of the drainage system. Then, typical rainfall events or actual monitored rainfall events are used as the model's driving conditions to run the model and obtain and output the water levels at each monitoring node at different times. With node traffic and topological connectivity Time series data, Indicates the node number. The simulation time step is... The total simulation time is Based on the pipeline topology and simulation identification results, network connectivity information such as the number of normal connected edges at each moment is statistically analyzed to form a simulation time series dataset.

[0010] Step 2 uses the simulation results from Step 1 to determine the nodes. Whether a node has failed is determined, and a node failure time series is generated. The formula for determining node failure is as follows:

[0011]

[0012] For nodes exist The water level at any given time For nodes Maximum permissible normal operating water level.

[0013] Step 3 involves constructing a semi-Markov state transition model for each node in the drainage network. This model characterizes the state evolution and residence time distribution of nodes under rainfall disturbances, and couples these processes through a cascading propagation mechanism between nodes to simulate the cascading failure of the drainage network. The specific node states are defined as follows:

[0014] Under normal operating conditions, the drainage capacity of the drainage node is stable, and the water level and flow rate of the node are in an ideal state.

[0015] : Minor damage condition, with a slight rise in water level or flow rate nearing the maximum at the drainage node, but still maintaining most of the drainage function.

[0016] : Moderate fault condition, the water level or flow rate at the drainage node exceeds the maximum limit, the node is overloaded and the water delivery capacity is significantly reduced.

[0017] : Severe fault condition. The drainage function of the drainage node is severely impaired and it stops working.

[0018] Each node The state is The state transition follows the probability matrix. :

[0019]

[0020] The dwell time of a node state follows a Weibull distribution:

[0021]

[0022] The resulting semi-Markov model allows for cross-level state transitions in the drainage network. And when the nodes... When a node fails The impact is as follows:

[0023]

[0024] in, For nodes After failure node Update traffic, Let be the cascade propagation coefficient, if the node With nodes If they are directly adjacent, then Otherwise, it is 0. Based on this, an iterative closed loop is formed by combining the state evolution probability and time of the drainage network nodes output by the semi-Markov model with the hydraulic feasibility and performance feedback output by the simulation.

[0025] Step 4 calculates the flow performance of the regional drainage network at each moment based on the node flow rate, node water level, and node connectivity data output from Step 1. Water level performance and connectivity performance This allows us to obtain the comprehensive performance of the drainage network in the area at every moment. .

[0026] The specific formula for calculating the flow performance of the regional drainage pipe network is as follows:

[0027]

[0028]

[0029] In the formula, For nodes Traffic performance, For the flow performance of the regional drainage pipe network, For nodes exist Flow rate at any moment For nodes Maximum allowed normal operating traffic This represents the total number of nodes in the regional drainage network.

[0030] The formula for calculating the water level performance of the regional drainage network is as follows:

[0031]

[0032] In the formula, for The number of nodes in the drainage network whose water level does not exceed the maximum water level of that node at any given time.

[0033] The formula for calculating the connectivity performance of a regional drainage network is as follows:

[0034]

[0035] In the formula, for The number of normally connected edges within the drainage pipe network at all times. This represents the total number of edges in the drainage network.

[0036] The formula for combining the three factors into a comprehensive performance is as follows:

[0037]

[0038] Step 5, based on the comprehensive performance of the drainage network obtained in Step 4, identifies key moments and their corresponding comprehensive performance values:

[0039] Disturbance occurrence time At that time, the comprehensive performance value of the drainage pipe network was When the threshold is broken At that time, the comprehensive performance value of the drainage pipe network was The moment of lowest performance At that time, the comprehensive performance value of the drainage pipe network was Performance recovered to a stable point At that time, the comprehensive performance value of the drainage pipe network was .

[0040] Calculate resistance and toughness The formula is as follows:

[0041]

[0042] Calculate the absorption toughness The formula is as follows:

[0043]

[0044] Calculate recovery resilience The formula is as follows:

[0045]

[0046] The formula for calculating the overall toughness of a drainage pipe network is as follows:

[0047]

[0048] In the formula, , , The three-stage resilience weights are determined based on the decision-makers' expected goals for the drainage network. Attached Figure Description

[0049] Figure 1 This is an abstract with attached figures.

[0050] Figure 2 This is a simulation model of a community in Wuhou District, Chengdu.

[0051] Figure 3 This is a chart showing the hourly rainfall statistics for Wuhou District, Chengdu, from July 11th to 12th, 2023.

[0052] Figure 4 This is a graph showing the performance values ​​of the drainage system and the overall performance evaluation results. Detailed Implementation

[0053] To facilitate understanding of the present invention and in conjunction with the accompanying drawings, a detailed description is provided below using the drainage pipe network of Wuhou District, Chengdu City as an example. The content described in this example is only for explaining the calculation method and evaluation process of the present invention; well-known technologies and data not detailed herein can be processed using conventional methods.

[0054] Step 1: This embodiment uses a stormwater dynamic simulation model for simulation, and dynamic waves are used for hydraulic solution. The catchment area of ​​the study area is approximately 80.3 ha, the pipe network contains 83 nodes, numbered J1–J83, and 85 pipes. The simulation period is from 00:00 on July 11, 2023 to 23:00 on July 12, 2023, with a discrete time step of [missing information]. The simulation lasts for 1 hour, and the specific simulation model is as follows: Figure 2 As shown.

[0055] Rainfall process such as Figure 3 As shown, the hourly rainfall record reflects the variation characteristics of a rainfall event, with a peak of 120 mm / h (July 11, 2023, 06:00), and a 48-hour cumulative rainfall of 860.5 mm. The simulation outputs the water level at each node at each time point. ,flow And the connectivity of the pipes / network, used for subsequent performance metric calculations.

[0056] Step 2: In this embodiment, the node failure determination rule is: once the node water level exceeds the water level threshold... Or the traffic exceeds the traffic threshold The node is considered failed upon reaching a threshold value, which is a preset threshold given in Step 5 of the embodiment. Node failure is equivalent to the node completely losing its drainage capacity; a failed node will no longer be able to drain water. The disturbance occurs at the following time. It is 01:00 on July 11, 2023.

[0057] Step 3: Analyze the 83 nodes using the MCMC method to identify the node set J1–J5 most likely to trigger cascading failure. Node status. The transitions follow the state transition probability matrix as shown in Table 1. The state duration follows a Weibull distribution, and the shape parameter... Scale parameters The time unit is 1 hour.

[0058] Table 1. Node state transition probability matrix of the drainage pipe network system in the embodiment

[0059] state 0.85 0.10 0.03 0.02 0.00 0.80 0.15 0.05 0.00 0.00 0.75 0.25 0.00 0.00 0.00 1.00

[0060] Step 4: In this embodiment, the flow rate, water level, and pipeline connectivity status at each time step are extracted from the SWMM simulation model, and then substituted into the formula to calculate the flow performance. Water level performance Connectivity performance and overall performance The example demonstrates a scenario where no intervention is taken after a failure of nodes J1-J5 predicted in Step 3 in a drainage network system. The final performance evaluation results are as follows: Figure 4 As shown.

[0061] Step 5: Combine the comprehensive performance of the drainage network system at each moment obtained in Step 3. According to the time of the disturbance With threshold And the recovery criteria, the three-stage resilience critical moments of this embodiment are shown in Table 2:

[0062] Table 2. Key moment parameters in the three-stage toughness calculation of Example 3

[0063] time meaning When does the drainage network disturbance occur? First time falling below the threshold 2023-07-11 02:00 During the observation process minimum value 2023-07-11 07:00 Recovery (above the threshold for 3 consecutive hours) 2023-07-12 23:00

[0064] Due to the original nature of this embodiment Since the data is discrete per hour, a step size of [missing value] is used. The method uses discrete summation rather than continuous integration. The specific discrete summation approximate integral calculation of the three-stage resilience formula is as follows:

[0065]

[0066]

[0067]

[0068] In this embodiment, the three-stage resilience weights are all taken as... The overall resilience is:

[0069]

Claims

1. A method for multi-stage resilience assessment of sewer networks based on an integrated performance indicator, characterized in that, include: Step 1: Construct a simulation model of the drainage pipe network in the study area and set up rainfall scenarios; Step 2: Identify node failure events based on node water level and flow thresholds; Step 3: Combine simulation and semi-Markov model to form a cascading failure simulation model; Step 4: Construct comprehensive performance indicators for the drainage network and classify the discrete states of the drainage network based on its comprehensive performance. Step 5: Use the comprehensive performance index built in Step 4 to evaluate the three-stage toughness and overall toughness of the drainage network.

2. Step 4 of the method according to claim 1, characterized in that: The overall performance of a drainage network is a function reflecting the flow rate, water level, and connectivity status of each node, encompassing flow performance, water level performance, and connectivity performance. The formula for the flow performance of a regional drainage network can be expressed as: in, For nodes Traffic performance, For the flow performance of drainage pipe network, For nodes At any moment Traffic, For nodes Maximum allowed normal operating traffic This represents the total number of nodes in the regional drainage network. The formula for calculating the water level performance of a regional pipe network can be expressed as: in, For water level performance, For a moment The number of nodes in the drainage network whose water level does not exceed the maximum water level of that node; The formula for calculating the connectivity performance of a regional pipe network can be expressed as: in, For the connectivity performance of the drainage pipe network, For a moment The number of normal connection edges within the drainage pipe network This represents the total number of edges in the drainage pipe network. Combining the three into a comprehensive performance:

3. Step 5 of the method according to claim 1, characterized in that: The overall resilience of drainage pipe networks includes three stages: resistance resilience, absorption resilience, and recovery resilience. Resistance resilience measures the magnitude of performance drop, absorption resilience measures the absorption capacity from the threshold to the lowest point, and recovery resilience measures the degree and speed of recovery from the lowest point to recovery. At the moment of disturbance Corresponding comprehensive performance value When the threshold is broken Corresponding comprehensive performance value Lowest performance moment Corresponding comprehensive performance value Performance recovered to a stable point Corresponding comprehensive performance value The resistance toughness, absorption toughness, recovery toughness and comprehensive toughness are calculated using the comprehensive performance of the drainage network obtained in Step 4. Specifically, resistance toughness can be calculated as: Among them, the time when the disturbance occurs The corresponding overall performance is , This represents the minimum value of the overall performance of the drainage network from the moment the disturbance begins until the overall performance recovers to a stable level. Absorbed toughness can be calculated as follows: in, The safety threshold representing the overall performance of the drainage pipe network. This indicates the moment when the overall performance of the drainage network first falls below the threshold. Until the moment of final stabilization The integral area between them; The recovery of resilience can be calculated as follows: in, This indicates that the drainage network has returned to a stable state. The corresponding comprehensive performance value at that time This indicates that the overall performance of the drainage network has reached its minimum value. The corresponding moment; The overall resilience of the drainage pipe network can be calculated as follows: in, , , The three-stage resilience weights are determined based on the decision-makers' expected goals for the drainage network.

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