Urban gas pipe network anti-seismic toughness curve establishing method based on Monte Carlo simulation

Abstract

The invention discloses a method for establishing an anti-seismic toughness curve of an urban gas pipe network based on Monte Carlo simulation. The method comprises the following steps: establishing a seismic motion prediction equation; acquiring basic data of the urban gas pipe network, and predicting seismic oscillation parameters of the urban gas pipe network; randomly sampling seismic oscillation parameters of the urban gas pipe network based on Monte Carlo simulation, and calculating the failure probability of each gate station and the failure probability of each pipeline in the urban gas pipe network; judging whether each gate station fails or not; determining the number of damage points on each failure pipeline, randomly distributing damage types to each damage point, and generating a gas pipe network damage network; and simulating the repair process of the damaged network of the gas pipe network to obtain a toughness curve of different attributes of the gas pipe network along with time change. The method is used for solving the problem that in the prior art, the recovery effect of the urban gas pipe network after an earthquake is difficult to quantify and evaluate, a complete urban gas pipe network anti-seismic toughness quantitative evaluation process can be formed, and the aim of evaluating the anti-seismic toughness of the urban gas pipe network more comprehensively is achieved.

Description

Technical Field

[0001] The present invention relates to the field of seismic performance research of urban gas pipe networks, and specifically relates to a method for establishing a seismic resilience curve of urban gas pipe networks based on Monte Carlo simulation. Background Art

[0002] The increase in natural gas production and the continuous construction of urban gas pipe networks have promoted the increase in gas utilization rate. Along with this, there comes the problem of natural gas transmission safety. The urban gas pipe network system is a major component of natural gas transmission and distribution. Therefore, the safe operation of urban gas pipe networks is an important part of energy security. The damage of earthquakes to urban gas pipe networks is particularly prominent. Earthquakes have the characteristics of suddenness, unpredictability, wide influence range, great destructiveness, and derivativeness. In the early urban planning, seismic factors were not fully incorporated, making the gas pipe networks show great vulnerability under earthquake shocks, threatening the safety and stability of the city. Facing natural disasters such as earthquakes with randomness and strong destructiveness, relying solely on the passive treatment method after the earthquake cannot effectively reduce the damage caused by earthquakes, and its emergency handling level and post-earthquake rescue ability both urgently need to be improved. Therefore, the research on the seismic resilience of urban gas pipe networks aims to improve their response and recovery abilities in disasters such as earthquakes by strengthening the seismic design and emergency capabilities of the pipe networks, and thus ensure the safe gas use environment for urban residents.

[0003] The seismic resilience of urban gas pipe networks can be defined as: under earthquake disturbances, the gas pipe network system maintains or quickly restores the gas use function of users, as well as the adaptability in the face of uncertainties at each stage. In the prior art, for the research on the seismic resilience of urban gas pipe networks, the mainstream methods mainly focus on constructing a resilience assessment system or a resilience theory research framework. However, these methods generally have certain subjectivity, lack prominent stage characteristics, consider the interactive effects of multiple factors weakly, and cannot effectively handle disaster uncertainties.

[0004] The resilience curve is an embodiment of the development of system resilience measurement towards quantification and visualization. It can show the whole process of the response - recovery of the pipe network system from the occurrence to the end of the disturbance. The degree of decline, the degree of rise, and the process time of the curve respectively reflect the vulnerability, resilience, and robustness of the pipe network system. By comparing with the system function baseline, the impact of the disturbance can be evaluated. However, in the prior art, there is no comprehensive and effective method for establishing the seismic resilience curve of urban gas pipe networks, making it difficult to quantify and evaluate the recovery effect of urban gas pipe networks after earthquakes. Summary of the Invention

[0005] The present invention provides a method for establishing the seismic resilience curve of urban gas pipe networks based on Monte Carlo simulation, aiming to solve the problem that there is no comprehensive and effective method for establishing the seismic resilience curve of urban gas pipe networks in the prior art, making it difficult to quantify and evaluate the recovery effect of urban gas pipe networks after earthquakes, and realizing the formation of a complete quantitative evaluation process for the seismic resilience of urban gas pipe networks, so as to more comprehensively evaluate the seismic resilience of urban gas pipe networks.

[0006] The present invention is realized through the following technical solutions:

[0007] A method for establishing the seismic resilience curve of urban gas pipe networks based on Monte Carlo simulation includes the following steps:

[0008] S1. Establish ground motion prediction equations under different earthquake magnitudes and site conditions;

[0009] S2. Obtain the basic data of the urban gas pipe network, select the matching ground motion prediction equation, and predict the ground motion parameters of the urban gas pipe network;

[0010] S3. Randomly sample the ground motion parameters of the urban gas pipe network based on Monte Carlo simulation, and calculate the failure probabilities of each gas station and pipeline in the urban gas pipe network;

[0011] S4. Determine whether each gas station fails;

[0012] S5. Determine the number of damage points on each failed pipeline, randomly assign damage types to each damage point, and generate a damaged network of the gas pipe network;

[0013] S6. Simulate the repair process of the damaged network of the gas pipe network to obtain the resilience curve of different attributes of the gas pipe network changing with time.

[0014] Aiming at the problem that there is no comprehensive and effective method for establishing the seismic resilience curve of urban gas pipe networks in the prior art and it is difficult to quantify and evaluate the recovery effect of urban gas pipe networks after earthquakes, the present invention proposes a method for establishing the seismic resilience curve of urban gas pipe networks based on Monte Carlo simulation. This method first establishes ground motion prediction equations under different earthquake magnitudes and site conditions for standby. When it is necessary to establish the seismic resilience curve of a specified gas pipe network, obtain its basic data, correspondingly select the matching ground motion prediction equation, and predict the ground motion parameters of the urban gas pipe network based on the ground motion prediction equation. Then, randomly sample the ground motion parameters of the urban gas pipe network based on Monte Carlo simulation.

[0015] The urban gas pipeline network is not only a network composed of pipelines / lines, but also includes some gate stations that play a role in pressure regulation in the pipeline network. Pipelines and gate stations are important node and edge units in the whole system. Therefore, in this application, the gate stations and pipelines are divided into two parts and analyzed as important components of the urban gas pipeline network. Specifically, in this application, the failure probabilities of each gate station and pipeline in the urban gas pipeline network are calculated according to the sampling results of ground motion parameters. For the gate stations, it is directly determined whether each gate station fails. For the corresponding pipelines, first, the number of damage points on each failed pipeline is determined, and then the damage types are randomly assigned to each damage point to generate a damaged network of the gas pipeline network. Thus, an equivalent model of the seismic damage failure probability of the urban gas pipeline network can be obtained. On this basis, the repair process of the damaged network of the gas pipeline network is simulated, and then the resilience curves of different attributes of the gas pipeline network changing with time are obtained.

[0016] This application solves the problems in the prior art that it is difficult to comprehensively and effectively establish the seismic resilience curve of the urban gas pipeline network and it is difficult to quantify and evaluate the recovery effect of the urban gas pipeline network after an earthquake. It provides a complete set of seismic resilience quantification processes for the urban gas pipeline network, which is beneficial to more comprehensively evaluate the seismic resilience of the urban gas pipeline network and is beneficial to formulating targeted earthquake disaster prevention and control plans for the urban gas pipeline network.

[0017] Further, the ground motion prediction equation is:

[0018] lgY = C1 + C2·M w + C3·M w 2 + C4lg[R + C5·exp(C6·M w )] + ε;

[0019] In the formula: Y is the target ground motion parameter; M w is the moment magnitude; R is the epicentral distance; C1, C2, C3, C4, C5 and C6 are all constants; ε is an uncertain random variable, obeying the normal distribution with a mean of 0 and a standard deviation of σlg(Y), where σ is the mean square deviation of the overall sample.

[0020] In the ground motion prediction equation of this scheme, the moment magnitude M w parameter is used as the input. Compared with the most commonly used surface wave magnitude, the relationship between the moment magnitude and the earthquake physical process is more direct, which is beneficial to reducing the occurrence probability of the magnitude saturation effect and then improving the prediction accuracy of the ground motion parameters.

[0021] Further, the ground motion parameters include: peak ground acceleration PGA, peak ground velocity PGV and permanent ground displacement PGD.

[0022] The peak ground acceleration (PGA) is the core parameter that determines the damage degree of gas pipeline networks during earthquakes. It represents the maximum acceleration when seismic waves reach the ground and directly reflects the instantaneous force on the ground structure. A higher PGA means stronger seismic forces, so gas pipeline networks are more likely to rupture and experience structural instability. Therefore, during the epicenter stage, the magnitude of PGA directly affects the vulnerability of gas pipeline networks and is an important basis for assessing the damage degree. Thus, PGA is one of the necessary ground motion parameters in this solution.

[0023] The peak ground velocity (PGV) reflects the propagation speed of seismic waves and is an important parameter that determines the damage range of gas pipeline networks during the epicenter stage. PGV not only affects physical damage but also determines the scale of the damaged area and the difficulty of repair. Therefore, it is crucial in the resilience assessment and is also one of the necessary ground motion parameters in this solution.

[0024] This solution also introduces the permanent ground displacement (PGD) as one of the necessary ground motion parameters, which can be used as a key parameter reflecting the gas supply stability and plays an important role in subsequent calculations of the failure probability.

[0025] Furthermore, the failure probability of the gate station is calculated by the following formula:

[0026] P 门站 = 1 - (1 - P 储气罐 ) × (1 - P 计量调压间 );

[0027]

[0028] Where: P 门站 is the failure probability of the gate station; P 储气罐 is the failure probability of the gas storage tank facility; P 储气罐 is the failure probability of the metering and pressure regulating room facility; PGA is the peak ground acceleration.

[0029] This solution uses PGA as the ground motion parameter to control the failure of gas gate stations. As a parameter describing the earthquake intensity, PGA directly reflects the instantaneous maximum acceleration on the ground under ground motion and has intuitiveness and easy accessibility. Therefore, using PGA as the control parameter for gate station failure helps to more accurately characterize the direct impact of ground motion on the gate station structure. This solution divides the gate station failure into two working conditions: gas storage tank failure and metering and pressure regulating room failure, which can achieve rapid quantification of the gate station failure probability.

[0030] Furthermore, the failure probability of the pipeline is calculated by the following formula:

[0031] P 管线 = 1 - (1 - P f1 )·(1 - P f2 );

[0032]

[0033] R f1 = 0.002416 × PGV × K1;

[0034] R f2 = 2.5829 × PGD 0.319 × K2;

[0035] Where: P 管线 is the pipeline failure probability; P f1 is the connected uncertainty failure probability; P f2 is the gas supply uncertainty failure probability; L is the pipeline length; R f1 is the average earthquake damage rate of connected uncertainty; R f2 is the average earthquake damage rate of gas supply uncertainty; PGV is the peak ground velocity; PGD is the permanent ground displacement; K1 is the adjustment coefficient related to PGV; K2 is the adjustment coefficient related to PGD.

[0036] During the research process, the inventor team of this case found that seismic waves propagate from the earthquake source to the surface soil layer, causing ground deformation. When the ground deforms, the soil drives the pipeline to move, and the pipeline is damaged during the movement. In this process, there are two situations: one is the deformation and damage of the pipeline caused by ground movement. In this process, PGV has a significant impact on the gas pipeline, because PGV directly reflects the ground velocity change caused by the propagation of seismic waves. The greater the ground vibration amplitude, the stronger the force and strain on the gas pipeline, thus increasing the pipeline damage risk; the other is the pipeline damage caused by permanent ground displacement such as faults, sand liquefaction, and ground subsidence caused by earthquakes. In this process, PGD has a more significant impact on the gas pipeline, which will cause the gas pipeline to bear large displacements and shear forces. Therefore, if following the traditional technology and only relying on PGV to describe the failure uncertainty of the gas pipeline, there are great limitations in this application and it is difficult to comprehensively reflect the pipeline damage mechanism caused by earthquakes.

[0037] Based on the above research process, this solution creatively introduces the permanent ground displacement (PGD) as one of the key parameters affecting the pipeline failure probability, and combines it with the peak ground velocity (PGV). Starting from the two aspects of connected uncertainty and gas supply uncertainty, a new calculation method for the pipeline failure probability of urban gas pipeline networks is constructed, significantly improving the calculation accuracy of the pipeline failure probability.

[0038] Considering that the gate station facilities include various key equipment such as pressure regulating equipment, metering equipment, safety valves, filters, etc., there are significant differences in the bearing capacity, damage modes, and recovery times of different equipment under seismic action, making the overall failure of the gate station show strong uncertainty. If each equipment is modeled separately and its seismic performance, failure probability, and recovery process are considered, the calculation process will be extremely complex. It not only requires a large amount of equipment earthquake damage data as support but also needs to establish a multi-level and multi-variable probability model, resulting in a significant increase in the calculation amount and thus reducing the evaluation efficiency. To reduce the calculation complexity and reasonably characterize the overall failure probability of the gate station under limited data, this solution simplifies the gate station failure determination method, sets the failure situation of the gate station to follow a uniform distribution of 0 to 1, and thus significantly reduces the difficulty of determining gate station failure and improves the evaluation efficiency.

[0039] Further, the method for determining whether each gate station fails includes:

[0040] Randomly generate a determination value r for each gate station within the range of 0 to 1, and compare r with the gate station failure probability of this gate station:

[0041] If r < the gate station failure probability, determine that this gate station fails;

[0042] If r ≥ the gate station failure probability, determine that this gate station is operating normally.

[0043] In the case of pipeline damage caused by an earthquake, there may be multiple damage points on a single pipeline, and the damage forms at each damage point may vary. When analyzing the impact of an earthquake on gas pipelines, in some cases, the pipeline may experience bending deformation but still be able to maintain gas supply. Although such a situation may have a certain impact on the mechanical properties of the pipeline, it will not directly affect the gas supply function. Since this solution mainly focuses on the impact of pipeline connectivity on user gas consumption, only two failure types, namely leakage and fracture, are considered. The damage of pipelines during an earthquake is affected by various factors, and the complexity of the factors makes it difficult to accurately predict the specific damage form of the pipeline through a single deterministic method. Therefore, the random assignment method can reasonably reflect the random impact of the earthquake on the pipeline.

[0044] Further, the method for determining the number of damage points on each failed pipeline includes:

[0045] S501. Screen the pipelines with a pipeline failure probability greater than the set threshold and define them as potentially failed pipelines;

[0046] S502. Calculate the average damage point spacing D of the potentially failed pipelines i :

[0047]

[0048] In the formula: U is a random variable following a uniform distribution of 0 - 1; Rimax is the maximum value of R f1 and R f2 ; i represents the i-th potentially failed pipeline;

[0049] S503. Determine whether each potentially failed pipeline is damaged:

[0050] If L i > D i , then the i-th potentially failed pipeline is intact;

[0051] If L i ≤ D i , then the i-th potentially failed pipeline is damaged;

[0052] where L i is the length of the i-th potentially failed pipeline;

[0053] S504. Calculate the number of damage points H of the damaged potentially failed pipelines i : H i = L i / D i .

[0054] When the failure probability of the pipeline to be calculated is greater than the set threshold, that is, the seismic damage level of the pipeline reaches the level of severe damage or destruction, the possibility of failure of this pipeline is extremely high and requires key attention. This solution determines the number of damage points for these key attention pipelines to facilitate the subsequent random allocation of damage forms.

[0055] Furthermore, the method for simulating the repair process of the damaged gas pipeline network includes:

[0056] S601. Fix the repair time of the gate station at 3 days and repair the failed gate station;

[0057] S602. Determine the respective repair times when the pipeline damage types are leakage and fracture;

[0058] S603. Use a random function to generate the repair order of each damaged potentially failed pipeline, sample and assign values to the repair time, and repair each damaged potentially failed pipeline;

[0059] S604. Determine whether the damaged gas pipeline network has been repaired; if not, return to step S5 and re-randomly allocate the damage types to each damage point.

[0060] The uncertainty in the repair of urban gas pipe networks makes it difficult to formulate and execute repair plans, and it is even more difficult to predict the repair time and effect, thus affecting the overall recovery progress and efficiency of the gas supply system. According to the historical records of gas gate stations during domestic earthquakes, it is set that the repair of a gate station takes 3 days. For failed pipelines, this solution adopts a normal distribution model to randomly sample and simulate the post-earthquake pipeline repair time, which is more in line with the emergency repair rules.

[0061] Furthermore, the method for obtaining the resilience curves of different attributes of the gas pipe network changing over time includes:

[0062] S605. Determine the seismic resilience attribute parameters of the gas pipe network; the seismic resilience attribute parameters include: technical attributes, organizational attributes, social attributes, and economic attributes;

[0063] S606. Establish a technical attribute resilience curve, an organizational attribute resilience curve, a social attribute resilience curve, and an economic attribute resilience curve respectively.

[0064] Urban gas pipe networks are not only affected by the characteristics of the pipe network itself and earthquakes but also related to the way of human intervention. Using a single attribute is difficult to comprehensively reflect its recovery ability, and the evaluation results obtained from different attributes may be inconsistent or even contradictory. Therefore, this solution comprehensively and efficiently quantifies the multi-attribute resilience of urban gas pipe networks in the disturbance, response, and recovery stages from four aspects: organization, technology, society, and economy. Among them, technical attributes reflect the physical performance change process of gas pipe network units and are the core of the seismic resilience of gas pipe networks; organizational attributes reflect the emergency response ability and resource scheduling efficiency of gas pipe networks in earthquake disasters; social attributes reflect the impact of gas pipe networks as social infrastructure on the population and social functions; economic attributes reflect the economic losses of gas pipe networks in earthquake disasters and their ability to restore economic balance.

[0065] Furthermore, it also includes:

[0066] S7. Based on the resilience curve, calculate the seismic resilience index:

[0067] TRT = t k - t0;

[0068]

[0069] In the formula: TRT is the recovery time; t k is the moment when the gas pipe network is completely restored; t0 is the moment when the repair of the gas pipe network starts;

[0070] SRT is the centroid of the recovery trajectory; Q(t) represents the resilience curve; Δt represents the time interval;

[0071] Re is the degree of network redundancy; Q(T)2 represents the post-earthquake performance of the organizational attributes of the gas pipeline network; Q(T)1 represents the post-earthquake performance of the technical attributes of the gas pipeline network;

[0072] R is the resilience; N(t) is the performance evaluation index of the seismic resilience attribute parameters corresponding to the gas pipeline network during normal operation at time t; N is the number of simulations.

[0073] The seismic resilience curve of the urban gas pipeline network can visualize the resilience level of the pipeline network, but there is still room for improvement in its quantification. In order to better quantify the seismic resilience of the urban gas pipeline network, this scheme proposes corresponding seismic resilience indicators for analysis.

[0074] Among them:

[0075] The recovery time TRT is used to quantify the length of time for the urban gas pipeline network to recover its performance, which is related to the recovery time of the seismic resilience influencing factors, that is, the time span of the recovery process. A small TRT value indicates a short system recovery time, reflecting the ability of the gas pipeline network to quickly recover after a disaster; a large TRT value indicates a longer system recovery process, indicating a weaker recovery ability. By analyzing TRT, the recovery speed of the system under different earthquake conditions and its influencing factors can be identified.

[0076] The centroid of the recovery trajectory SRT can be understood as the centroid position of the area under the corresponding resilience curve, aiming to reflect the recovery efficiency of the system. SRT is closely related to the process variables such as the gas regulation and supply guarantee ability, maintenance speed and quality, etc., which reflect the recovery performance of the pipeline network. When the recovery time (TRT) is the same, the larger the SRT value, the lower the repair efficiency of the system during the recovery process; on the contrary, the smaller the SRT value, the higher the performance recovery efficiency of the system. SRT can provide a quantitative analysis of the efficiency performance of the system during the post-earthquake recovery period, which is convenient for comparing the recovery effects of different strategies.

[0077] The redundancy degree Re can be understood as the ratio of the post-earthquake performance indexes of the organizational attributes and technical attributes, and is used to quantify the quality of the network structure of the urban gas system under the set earthquake conditions. This index is closely related to the density of the gas pipeline network and the rationality of the pipeline network layout. The higher the Re value, the more excellent the structural performance of the network, the stronger the stability and shock resistance of the system during an earthquake, and thus it helps to enhance the overall resilience of the system.

[0078] The resilience R is used to comprehensively measure the seismic resistance and recovery ability of the gas pipeline network. The larger the R value, the stronger the seismic resilience of the gas system, and it can better cope with earthquake shocks and recover to the pre-earthquake state. The resilience R can provide key guidance for the optimal design and emergency management of the gas system.

[0079] This solution takes factors such as the density of the gas pipeline network, the rationality of the pipeline network layout, the gas regulation and supply guarantee ability, the maintenance speed and quality, and the recovery time during the epicenter and post-earthquake stages as the core impact indicators to quantify the key features of the system. Through analysis, four seismic resilience evaluation indicators, namely the recovery time (TRT), the centroid of the recovery trajectory (SRT), the redundancy degree (Re), and the resilience (R), are established to provide data support for the seismic design and improvement of urban gas pipeline networks.

[0080] Compared with the prior art, the present invention has at least the following advantages and beneficial effects:

[0081] 1. The method for establishing the seismic resilience curve of urban gas pipeline networks based on Monte Carlo simulation in the present invention solves the problems in the prior art that it is difficult to comprehensively and effectively establish the seismic resilience curve of urban gas pipeline networks and it is difficult to quantify and evaluate the post-earthquake recovery effect of urban gas pipeline networks. It provides a complete set of quantitative processes for the seismic resilience of urban gas pipeline networks, which is beneficial to more comprehensively evaluate the seismic resilience of urban gas pipeline networks and is beneficial to formulating targeted earthquake disaster prevention and control measures for urban gas pipeline networks.

[0082] 2. The method for establishing the seismic resilience curve of urban gas pipeline networks based on Monte Carlo simulation in the present invention introduces the permanent ground displacement (PGD) as one of the key parameters affecting the probability of pipeline failure, and combines it with the peak ground velocity (PGV). Starting from the two aspects of connectivity uncertainty and gas supply uncertainty, a new calculation method for the probability of pipeline failure of urban gas pipeline networks is constructed, which significantly improves the calculation accuracy of the probability of pipeline failure.

[0083] 3. The method for establishing the seismic resilience curve of urban gas pipeline networks based on Monte Carlo simulation in the present invention comprehensively and efficiently quantitatively evaluates the multi-attribute resilience of urban gas pipeline networks in the disturbance, response, and recovery stages from four aspects: organization, technology, society, and economy.

[0084] 4. The method for establishing the seismic resilience curve of urban gas pipeline networks based on Monte Carlo simulation in the present invention establishes four seismic resilience evaluation indicators, namely the recovery time, the centroid of the trajectory, the redundancy degree, and the resilience, to provide data support for the seismic design and improvement of urban gas pipeline networks. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, constitute a part of this application, and do not limit the embodiments of the present invention. In the drawings:

[0086] Figure 1 is a schematic flowchart of a specific embodiment of the present invention;

[0087] Figure 2 is a simplified diagram of the urban gas pipeline network in a specific embodiment of the present invention;

[0088] Figure 3 Schematic diagram of the post-earthquake performance of the urban gas pipeline network in the specific embodiment of the present invention;

[0089] Figure 4 Technical property toughness curve in the specific embodiment of the present invention;

[0090] Figure 5 Organizational property toughness curve in the specific embodiment of the present invention;

[0091] Figure 6 Social property toughness curve in the specific embodiment of the present invention;

[0092] Figure 7 Economic property toughness curve in the specific embodiment of the present invention. Specific implementation manners

[0093] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below in conjunction with the embodiments and the drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and do not limit the present invention. In the description of the present application, it should be understood that the orientation or positional relationship indicated by terms such as "front", "rear", "left", "right", "up", "down", "vertical", "horizontal", "high", "low", "inner", "outer", etc. is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the protection scope of the present application.

[0094] Embodiment 1:

[0095] As Figure 1 shown, a method for establishing the seismic resilience curve of an urban gas pipeline network based on Monte Carlo simulation includes the following steps:

[0096] S1. Establish ground motion prediction equations under different earthquake magnitudes and site conditions:

[0097] lgY = C1 + C2·M w + C3·M w 2 + C4lg[R + C5·exp(C6·M w )] + ε;

[0098] In the formula: Y is the target ground motion parameter; M w is the moment magnitude; R is the epicentral distance; C1, C2, C3, C4, C5 and C6 are all constants; ε is an uncertain random variable, subject to a normal distribution with a mean of 0 and a standard deviation of σlg(Y), where σ is the mean square deviation of the overall sample.

[0099] S2. Obtain the basic data of the urban gas pipeline network, select the matching ground motion prediction equation, and predict the ground motion parameters of the urban gas pipeline network. The ground motion parameters include: peak ground acceleration PGA, peak ground velocity PGV, and permanent ground displacement PGD.

[0100] S3. Randomly sample the ground motion parameters of the urban gas pipeline network based on Monte Carlo simulation, and calculate the failure probabilities of each gas station and pipeline in the urban gas pipeline network.

[0101] Among them, the failure probability of the gas station is calculated by the following formula:

[0102] P 门站 = 1 - (1 - P 储气罐 ) × (1 - P 计量调压间 );

[0103]

[0104] In the formula: P 门站 is the failure probability of the gas station; P 储气罐 is the failure probability of the gas storage tank facility; P 储气罐 is the failure probability of the metering and pressure regulating room facility; PGA is the peak ground acceleration.

[0105] Among them, the failure probability of the pipeline is calculated by the following formula:

[0106] P 管线 = 1 - (1 - P f1 ) · (1 - P f2 );

[0107]

[0108] R f1 = 0.002416 × PGV × K1;

[0109] R f2 = 2.5829 × PGD 0.319 × K2;

[0110] In the formula: P 管线 is the failure probability of the pipeline; P f1 is the failure probability of connectivity uncertainty; P f2 is the failure probability of gas supply uncertainty; L is the pipeline length; R f1 is the average earthquake damage rate of connectivity uncertainty; R f2 is the average earthquake damage rate of gas supply uncertainty; PGV is the peak ground velocity; PGD is the permanent ground displacement; K1 is the adjustment coefficient related to PGV; K2 is the adjustment coefficient related to PGD.

[0111] S4. Determine whether each gate station fails:

[0112] Randomly generate a judgment value r within the range of 0 to 1 for each gate station, and compare r with the gate station failure probability of that gate station:

[0113] If r < the gate station failure probability, determine that the gate station fails;

[0114] If r ≥ the gate station failure probability, determine that the gate station is operating normally.

[0115] S5. Determine the number of damage points on each failed pipeline:

[0116] Screen the pipelines with a pipeline failure probability greater than the set threshold, and define them as potentially failed pipelines; the set threshold in this embodiment is taken as 0.75;

[0117] Calculate the average distance D between damage points of potentially failed pipelines i :

[0118]

[0119] In the formula: U is a random variable subject to a uniform distribution of 0 - 1; R imax is the maximum value of R f1 , R f2 ; i represents the i-th potentially failed pipeline;

[0120] Judge whether each potentially failed pipeline is damaged:

[0121] If L i > D i , then the i-th potentially failed pipeline is intact;

[0122] If L i ≤ D i , then the i-th potentially failed pipeline is damaged;

[0123] Among them, L i is the length of the i-th potentially failed pipeline;

[0124] Calculate the number of damage points H of the damaged potentially failed pipelines i : H i = L i / D i .

[0125] After that, randomly assign damage types to each damage point to generate a damaged gas pipeline network.

[0126] S6. Simulate the repair process of the damaged gas pipeline network:

[0127] Fix the gate station repair time at 3 days and repair the failed gate stations;

[0128] Determine the respective repair times when the pipeline damage types are leakage and fracture;

[0129] Use a random function to generate the repair order of the possible failed pipelines for each damage, sample and assign values to the repair times, and repair the possible failed pipelines for each damage;

[0130] Judge whether the damaged gas pipeline network has been completely repaired; if not, return to step S5 and randomly reassign the damage types to each damage point.

[0131] After that, obtain the toughness curve of different attributes of the gas pipeline network changing with time through the following method:

[0132] Determine the seismic toughness attribute parameters of the gas pipeline network; the seismic toughness attribute parameters include: technical attributes, organizational attributes, social attributes, and economic attributes;

[0133] Establish a technical attribute toughness curve, an organizational attribute toughness curve, a social attribute toughness curve, and an economic attribute toughness curve respectively.

[0134] In addition, this embodiment also calculates the seismic toughness index based on the toughness curve:

[0135] TRT = t k - t0;

[0136]

[0137] Where: TRT is the recovery time; t k is the moment when the gas pipeline network is completely restored; t0 is the moment when the repair of the gas pipeline network starts;

[0138] SRT is the centroid of the recovery trajectory; Q(t) represents the toughness curve; Δt represents the time interval;

[0139] Re is the network redundancy degree; Q(T)2 represents the post-earthquake performance of the organizational attributes of the gas pipeline network; Q(T)1 represents the post-earthquake performance of the technical attributes of the gas pipeline network;

[0140] R is the restoring force; N(t) is the performance evaluation index of the seismic toughness attribute parameters corresponding to the gas pipeline network under normal operation at time t; N is the number of simulations.

[0141] Example 2:

[0142] Based on the method for establishing the seismic toughness curve of the urban gas pipeline network by Monte Carlo simulation, on the basis of Example 1:

[0143] This embodiment combines the existing basic theoretical framework and refers to the actual pipeline earthquake damage situation in China. For different pipe materials and pipe diameter characteristics, values are assigned to K1 and K2 according to the pipe materials and pipe diameters, as shown in Table 1.

[0144] Table 1 Assignment Table of K1 and K2

[0145]

[0146] Example 3:

[0147] A method for establishing the seismic resilience curve of urban gas pipeline networks based on Monte Carlo simulation. On the basis of Example 1 or 2, the technical attribute resilience curve, organizational attribute resilience curve, social attribute resilience curve, and economic attribute resilience curve are established through the technical attribute resilience function, organizational attribute resilience function, social attribute resilience function, and economic attribute resilience function respectively.

[0148] In this example:

[0149] The technical attribute resilience function is:

[0150] Q(t)1 = ω1·n s / N s +ω2·n p / N p ;

[0151] Where: Q(t)1 is the seismic resilience under technical attributes; N s , n s are the numbers of non-failed gate stations before and after the earthquake respectively; N p , n p are the numbers of non-failed pipelines before and after the earthquake respectively; w1 and w2 are the importance factors of the gate station and the pipeline respectively, satisfying w1 + w2 = 1.

[0152] The organizational attribute resilience function is:

[0153]

[0154] Where: Q(t)2 is the seismic resilience under organizational attributes; N pre is the number of users who can receive gas before the earthquake; n pos is the number of users who can receive gas after the earthquake.

[0155] The social attribute resilience function is:

[0156]

[0157] Where: Q(t)3 is the seismic resilience under social attributes; w i is the coefficient representing the importance degree of user i. For example, users such as hospitals, schools, shopping malls, and important transportation hubs take the value of 1.5, and ordinary residential users take the value of 1; n i is the population density covered by user i.

[0158] The economic attribute resilience function is:

[0159]

[0160] Where: Q(t)4 is the seismic toughness under economic attributes; I s The construction amount of the gate station of the urban gas pipeline network is in ten thousand yuan; j1 The construction cost of urban gas pipeline network, in ten thousand yuan / km; L i n p The length of each corresponding non-failed pipeline, in km; I j2 The amount required to repair a gate station, in ten thousand yuan; j3 The amount required to repair a pipeline, in ten thousand yuan; p The construction cost of the entire urban gas pipeline network, in ten thousand yuan.

[0161] Example 4:

[0162] This embodiment uses a gas pipeline network in a city in southwestern China, where earthquakes are frequent, as an example to establish a seismic toughness curve and calculate a seismic toughness index.

[0163] The city's town gas pipeline network is as follows Figure 2 As shown, the pipeline pressure is primarily high pressure (4.0 MPa), using steel and PE pipes. Currently, there are two gate stations, 131 node units, and 136 pipelines, totaling 83.437 km. Currently, the gas network has 287 users.

[0164] The city is located near the Longmenshan earthquake fault zone. Plate movement makes the area prone to earthquakes. The maximum magnitude of the earthquake is 7. The earthquake motion prediction equation established is:

[0165]

[0166] Where: ε1 obeys a normal distribution with a mean of 0 and a standard deviation of 0.7918; ε2 obeys a normal distribution with a mean of 0 and a standard deviation of 0.8643; ε3 obeys a normal distribution with a mean of 0 and a standard deviation of 0.9439.

[0167] This example performs a Monte Carlo simulation on each node in the target town gas network, sampling 10,000 times. Because the uncertainty of earthquake motion is taken into account, the PGA, PGV, and PGD obtained each time are different. Therefore, the median value of the earthquake motion parameters for each node is taken from a specific simulation to represent the seismic network status during that simulation. The PGA corresponding to the two gate stations in this town gas network is shown in Table 2:

[0168] Table 2 Gate station PGA values

[0169] Gate station node number Epicentral distance (km) PGA (g) 130 3.351559 0.455989508 131 10.86963 0.263199218

[0170] The PGV and PGD values of each pipe section of the urban gas pipeline network are obtained, and some results are shown in Table 3 as follows:

[0171] Table 3 PGV and PGD values of some pipelines in the urban gas pipeline network

[0172] Pipeline number Pipeline length (m) PGV (cm / s) PGD (cm) 1-2 34.209 60.286 55.067 1-130 611.783 62.100 53.780 1-4 427.165 60.545 56.580 2-3 606.036 61.282 56.086 2-40 249.207 59.052 54.983 3-4 306.242 61.541 57.598 3-6 321.847 63.053 56.614 4-5 35.131 61.374 58.281 5-6 677.292 62.886 57.297 5-71 316.116 64.074 56.745 6-7 1006.072 62.258 57.417 7-8 195.118 60.259 57.555 7-9 490.440 58.518 57.793

[0173] After that, the failure probability of the gate station is calculated as shown in Table 4:

[0174] Table 4 Failure probability of the gate station

[0175] Gate station node number PGA (g) Failure probability P 130 0.455989508 0.6655902 131 0.263199218 0.249103276

[0176] It can be seen from Table 4 that the failure probability of Gate Station No. 130 is higher than that of Gate Station No. 131. The reason is that Gate Station No. 130 is close to the seismic source, and the seismic ground motion intensity and related seismic ground motion parameter characteristics it receives are more significant, resulting in a greater impact on its seismic resistance ability.

[0177] In the case of steel pipes in this embodiment, take K1 = 0.08, K2 = 1.5×10 -4 ; in the case of PE pipes, take K1 = 0.05, K2 = 8×10 -5 . Accordingly, the failure probabilities of each pipeline are calculated, and some calculation results are shown in Table 5:

[0178] Table 5 Failure probabilities of some gas pipelines

[0179]

[0180] After that, according to the failure probabilities of each pipeline of the urban gas pipeline network obtained by calculation, the pipelines with P>0.75 are selected. It is considered that these pipelines are very likely to fail when an earthquake occurs. Calculate the lengths of the two damaged points and the number of damaged points of these pipelines, and the pipeline damage point results are shown in Table 6:

[0181] Table 6 Pipeline damage point records

[0182]

[0183]

[0184] So far, based on the above calculations, the failure conditions of each gate station and pipeline in the urban gas pipeline network under a certain magnitude 7 earthquake can be obtained as Figure 3 shown, Figure 3 The red area in it represents the failed facilities. It can be seen that Gate Station No. 130 fails, and a total of 18 pipelines such as 9-10 and 10-20 fail.

[0185] After that, simulate the repair process:

[0186] In this studied pipe network, the gate station No. 130 fails, and a total of 18 pipelines such as 9-10 and 10-20 fail. First, repair the gate station No. 130. Three days later, the gate station is completely repaired first, and part of the gas supply function is restored. After that, start to repair each failed pipeline until all pipelines are repaired, and the urban gas pipeline network returns to the initial state with good performance.

[0187] Finally, the technical attribute toughness curve, organizational attribute toughness curve, social attribute toughness curve, and economic attribute toughness curve are obtained as shown in Figure 4 、 Figure 5 、 Figure 6 and Figure 7 respectively.

[0188] In addition, this embodiment also calculates the seismic resilience index of the urban gas pipeline network:

[0189] (1) Recovery time of the target urban gas pipeline network: TRT = 223 - 6 = 217 h.

[0190] This result indicates that the recovery process of this pipeline network after an earthquake takes about 217 hours, which is about 9 days. The larger TRT value means that the recovery process of this system is relatively long, reflecting its relatively weak recovery ability. In response to this result, if the initial repair efficiency can be optimized or the seismic design of key facilities can be improved, the recovery time may be significantly shortened.

[0191] (2) Centroid of the recovery trajectory:

[0192] Based on the toughness curves of the four attributes, the centroid of the recovery trajectory under each attribute is calculated, and a comparative analysis is carried out to evaluate the influence of different attributes on the system recovery efficiency. The calculation results are shown in Table 7:

[0193] Table 7 SRT values under each attribute

[0194] Attribute SRT Technology 111.3501 Organization 111.4325 Society 111.4528 Economy 111.3043

[0195] It can be seen from the above table that the SRT values of the four attributes are relatively consistent. This may reflect that during the repair process of this urban gas pipeline network, the coordination among various attribute dimensions is relatively good, especially the effectiveness of resource scheduling and management.

[0196] (3) Redundancy degree:

[0197] In this embodiment, taking t = 6h, after an earthquake occurs, the performance level Q2(t = 6) = 85.72% under the organizational attribute of the urban gas pipeline network, and the performance level Q1(t = 6) = 68.75% under the technical attribute. Then the redundancy result Re = 85.72% / 68.75% = 1.25.

[0198] The relatively high value of the redundancy Re indicates that in the initial stage after the earthquake, the urban gas pipeline network has a strong standby capacity and an emergency fault tolerance mechanism.

[0199] (4) Resilience:

[0200] When the gas pipeline network is operating normally, the performance evaluation index values of each attribute are all 100%. The resilience R values under the four attributes are shown in Table 8:

[0201] Table 8 R values under each attribute

[0202] Attribute R Technology 0.8719 Organization 0.9148 Society 0.9344 Economy 0.7901

[0203] It can be seen from Table 8 that the resilience of the social attribute and the organizational attribute is relatively strong, especially the social attribute (R = 0.9344), which indicates that the pipeline network can quickly resume the gas supply service to the social population and key users after the earthquake. In contrast, the resilience of the economic attribute (R = 0.7901) is relatively weak, reflecting that the economic losses may be relatively significant, and there may be relatively high cost pressure during the recovery process.

[0204] It can be seen that according to the above calculation process, the seismic performance and its toughness level of the target urban gas pipeline network under the four attributes can be clearly and accurately grasped, thereby providing a scientific and reasonable basis for proposing phased measures to improve the seismic toughness of the gas pipeline network and for analyzing the applicability of seismic toughness measures, and at the same time, it can also provide an important reference for the seismic engineering design and maintenance of gas pipeline projects.

[0205] The specific implementation manners described above have further detailed the purpose, technical solutions, and beneficial effects of the present invention. It should be understood that the above description is only the specific implementation manners of the present invention and is not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

[0206] It should be noted that in this article, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device comprising a series of elements not only includes those elements, but also includes other elements not expressly listed, or elements inherent to such process, method, article or device. In addition, the term "connected" used in this article, without special explanation, can be directly connected or indirectly connected via other components.

Claims

1. A method for establishing the seismic resilience curve of urban gas pipeline networks based on Monte Carlo simulation, characterized in that It includes the following steps: S1. Establish ground motion prediction equations under different earthquake magnitudes and site conditions; S2. Obtain the basic data of urban gas pipeline networks, select the matching ground motion prediction equations, and predict the ground motion parameters of urban gas pipeline networks; S3. Randomly sample the ground motion parameters of urban gas pipeline networks based on Monte Carlo simulation, and calculate the failure probabilities of each gate station and pipeline in the urban gas pipeline network; S4. Determine whether each gate station fails; S5. Determine the number of damage points on each failed pipeline, randomly assign damage types to each damage point, and generate a damaged network of the gas pipeline network; S6. Simulate the repair process of the damaged network of the gas pipeline network to obtain the resilience curves of different attributes of the gas pipeline network changing with time.

2. The method for establishing the seismic resilience curve of urban gas pipeline network based on Monte Carlo simulation according to claim 1, characterized in that, The ground motion prediction equation is: lgY = C1 + C2·M w + C3·M w 2 + C4lg[R + C5·exp(C6·M w )] + ε; Where: Y is the target ground motion parameter; M w is the moment magnitude; R is the epicentral distance; C1, C2, C3, C4, C5, and C6 are all constants; ε is an uncertain random variable that follows a normal distribution with a mean of 0 and a standard deviation of σlg(Y), where σ is the mean square deviation of the overall sample.

3. The method for establishing the seismic resilience curve of urban gas pipeline networks based on Monte Carlo simulation according to claim 1, characterized in that The ground motion parameters include: peak ground acceleration, peak ground velocity, and permanent ground displacement.

4. The method for establishing the seismic resilience curve of urban gas pipeline networks based on Monte Carlo simulation according to claim 3, wherein, The failure probability of the gate station is calculated by the following formula: P 门站 = 1 - (1 - P 储气罐 ) × (1 - P 计量调压间 ); Where: P 门站 is the failure probability of the gate station; P 储气罐 is the failure probability of the facilities of the gas storage tank; P 储气罐 is the failure probability of the facilities of the metering and pressure regulating room; PGA is the peak ground acceleration of the earthquake.

5. The method for establishing the seismic resilience curve of urban gas pipeline network based on Monte Carlo simulation according to claim 3, characterized in that The failure probability of the pipeline is calculated by the following formula: P 管线 = 1 - (1 - P f1 )·(1 - P f2 ); R f1 = 0.002416 × PGV × K1; R f2 = 2.5829 × PGD 0.319 × K2; Where: P 管线 is the pipeline failure probability; P f1 is the connectivity uncertainty failure probability; P f2 is the gas supply uncertainty failure probability; L is the pipeline length; R f1 is the average earthquake damage rate of connectivity uncertainty; R f2 is the average earthquake damage rate of gas supply uncertainty; PGV is the peak ground velocity; PGD is the permanent ground displacement; K1 is the adjustment coefficient related to PGV; K2 is the adjustment coefficient related to PGD.

6. The method for establishing the seismic resilience curve of urban gas pipeline network based on Monte Carlo simulation according to claim 1, characterized in that, The method for determining whether each gate station fails includes: Randomly generate a judgment value r for each gate station within the range of 0 to 1, and compare r with the failure probability of the gate station: If r < the failure probability of the gate station, it is determined that the gate station fails; If r ≥ the failure probability of the gate station, it is determined that the gate station operates normally.

7. The method for establishing the seismic resilience curve of urban gas pipeline networks based on Monte Carlo simulation according to claim 5, wherein The method for determining the number of damage points on each failed pipeline includes: S501. Screen the pipelines with a pipeline failure probability greater than the set threshold and define them as potentially failed pipelines; S502. Calculate the average distance D between the damage points of the pipes that may fail i : where: U is a random variable subject to a uniform distribution of 0 - 1; R imax is the f1 maximum value among f2 R , R ; i represents the i-th possible failure pipeline; S503. Judge whether each potentially failed pipeline is damaged: If L i > D i , then the i-th potentially failed pipe is intact; If L i ≤ D i , then the i-th potentially failed pipe is damaged; where L i is the length of the i-th potentially failed pipeline; S504. Calculate the number of damage points H of the possibly failed pipes damaged i : H i = L i / D i .

8. The method for establishing the seismic resilience curve of urban gas pipeline networks based on Monte Carlo simulation according to claim 1, characterized in that The method for simulating the repair process of the damaged network of the gas pipeline network includes: S601. Fix the repair time of the gate station at 3 days and repair the failed gate station; S602. Determine the respective repair times when the pipeline damage types are leakage and fracture; S603. Use a random function to generate the repair order of each damaged potentially failed pipeline, sample and assign values to the repair time, and repair each damaged potentially failed pipeline; S604. Judge whether the damaged network of the gas pipeline network is completely repaired; if not, return to step S5 and randomly re-assign damage types to each damage point.

9. The method for establishing the seismic resilience curve of urban gas pipeline network based on Monte Carlo simulation according to claim 1, wherein The method for obtaining the resilience curves of different attributes of the gas pipeline network changing with time includes: S605. Determine the seismic resilience attribute parameters of the gas pipeline network; the seismic resilience attribute parameters include: technical attributes, organizational attributes, social attributes, and economic attributes; S606. Establish a technical attribute resilience curve, an organizational attribute resilience curve, a social attribute resilience curve, and an economic attribute resilience curve respectively.

10. The method for establishing the seismic resilience curve of urban gas pipeline network based on Monte Carlo simulation according to claim 9, wherein It also includes: S7. Calculate the seismic resilience index based on the resilience curve: TRT = t k - t0; Where: TRT is the recovery time; t k is the moment when the gas pipeline network is fully restored; t0 is the moment when the repair of the gas pipeline network starts; SRT is the centroid of the recovery trajectory; Q(t) represents the resilience curve; Δt represents the time interval; Re is the network redundancy degree; Q(T)2 represents the post-earthquake performance of the organizational attributes of the gas pipeline network; Q(T)1 represents the post-earthquake performance of the technical attributes of the gas pipeline network; R is the restoring force; N(t) is the performance evaluation index of the seismic resilience attribute parameters corresponding to the gas pipeline network operating normally at time t; N is the number of simulations.

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